Showing papers in "Theoretical Informatics and Applications in 2001"
TL;DR: A sharpening of the Parikh map- ping is introduced and an interesting in- terconnection between mirror images of words and inverses of matrices is established.
Abstract: In this paper we introduce a sharpening of the Parikh map- ping and investigate its basic properties. The new mapping is based on square matrices of a certain form. The classical Parikh vector appears in such a matrix as the second diagonal. However, the matrix prod- uct gives more information about a word than the Parikh vector. We characterize the matrix products and establish also an interesting in- terconnection between mirror images of words and inverses of matrices. Mathematics Subject Classification. 68Q45, 68Q70.
126 citations
TL;DR: This paper gives a semantical underpinning for a many- sorted modal logic associated with certain dynamical systems, like tran- sition systems, automata or classes in object-oriented languages, as coalgebras of so-called polynomial func- tors, built up from constants and identities, using products, coproducts and powersets.
Abstract: This paper gives a semantical underpinning for a many- sorted modal logic associated with certain dynamical systems, like tran- sition systems, automata or classes in object-oriented languages. These systems will be described as coalgebras of so-called polynomial func- tors, built up from constants and identities, using products, coproducts and powersets. The semantical account involves Boolean algebras with operators indexed by polynomial functors, called MBAOs, for Many- sorted Boolean Algebras with Operators, combining standard (categor- ical) models of modal logic and of many-sorted predicate logic. In this setting we will see Lindenbaum MBAO models as initial objects, and canonical coalgebraic models of maximally consistent sets of formulas as nal objects. They will be used to (re)prove completeness results, and Hennessey{Milner style characterisation results for the modal logic, rst established by Roiger. Mathematics Subject Classication. 03G05, 03G30, 06E25.
109 citations
TL;DR: This paper describes log-depth, polynomial size, logspace-uniform, i.e. , NC 1 circuit family for integer division, and shows that division is in logspace.
Abstract: Beame, Cook and Hoover were the first to exhibit a log-depth, polynomial size circuit family for integer division. However, the family was not logspace-uniform. In this paper we describe log-depth, polynomial size, logspace-uniform, i.e. , NC 1 circuit family for integer division. In particular, by a well-known result this shows that division is in logspace. We also refine the method of the paper to show that division is in dlogtime-uniform NC 1 .
103 citations
TL;DR: In this article, the succinctness of several kinds of unary automata was investigated by studying their state complexity in accepting the family {L m } of cyclic languages, where L m = {a km k ∈ N}.
Abstract: We investigate the succinctness of several kinds of unary automata by studying their state complexity in accepting the family {L m } of cyclic languages, where L m = {a km k ∈ N}. In particular, we show that, for any m, the number of states necessary and sufficient for accepting the unary language L m with isolated cut point on one-way probabilistic finite automata is p α1 1 +p α2 2 +...+p αs s , with p α1 1 p α2 2 ...p αs s being the factorization of m. To prove this result, we give a general state lower bound for accepting unary languages with isolated cut point on the one-way probabilistic model. Moreover, we exhibit one-way quantum finite automata that, for any m, accept L m with isolated cut point and only two states. These results are settled within a survey on unary automata aiming to compare the descriptional power of deterministic, nondeterministic, probabilistic and quantum paradigms.
40 citations
TL;DR: The notion of a k -synchronized sequence, where k is an integer larger than 1, is introduced and it is shown that theclass of k -automatic sequences is equal to the class of bounded k - synchronized sequences and that the class is strictly contained in that of k-regular sequences.
Abstract: We introduce the notion of a k -synchronized sequence, where k is an integer larger than 1. Roughly speaking, a sequence of natural numbers is said to be k -synchronized if its graph is represented, in base k , by a right synchronized rational relation. This is an intermediate notion between k -automatic and k -regular sequences. Indeed, we show that the class of k -automatic sequences is equal to the class of bounded k -synchronized sequences and that the class of k -synchronized sequences is strictly contained in that of k -regular sequences. Moreover, we show that equality of factors in a k -synchronized sequence is represented, in base k , by a right synchronized rational relation. This result allows us to prove that the separator sequence of a k -synchronized sequence is a k -synchronized sequence, too. This generalizes a previous result of Garel, concerning k -regularity of the separator sequences of sequences generated by iterating a uniform circular morphism.
39 citations
TL;DR: Abbott et al. as mentioned in this paper presented a framework for archeological investigation, interpretation, and cultural resource management in the Houston Highway District, which is based on the Gray Literature from the Lone Star State.
Abstract: Cite this Record Abbott, James T. (2001) \"Houston Area Geoarcheology: A Framework for Archeological Investigation, Interpretation, and Cultural Resource Management in the Houston Highway District,\" Index of Texas Archaeology: Open Access Gray Literature from the Lone Star State: Vol. 2001, Article 20. https://doi.org/ 10.21112/ita.2001.1.20 ISSN: 2475-9333 Available at: https://scholarworks.sfasu.edu/ita/vol2001/iss1/20
31 citations
TL;DR: The first two seasons were conducted by TxDOT archaeologists and the third was directed by personnel from the Center for Archaeological Research (CAR) of The University of Texas at San Antonio as discussed by the authors.
Abstract: Archaeological test excavations were undertaken at 4IBX126 on Culebra Creek to offset the impact from a proposed Texas Department of Transportation (TxDOT) highway improvement proj ect on Loop 1604 in northwest Bexar County. Archaeological investigations were conducted in three field seasons: the first two seasons were conducted by TxDOT archaeologists and the third was directed by personnel from the Center for Archaeological Research (CAR) of The University of Texas at San Antonio. During the three projects, 55 hand-dug units, 29 backhoe trenches, 36 shovel tests, and eight Gradall trenches were excavated. Seventeen features were recorded; 25 radiocarbon assays were conducted; over 59,000 lithic artifacts were recovered and analyzed; 1,655 liters of sediment float samples were processed; 3,337 kg of burned rock were analyzed; and nearly 300 g of fatmal material and 25 archaeomagnetic samples were analyzed. The testing revealed utilization of the site in the Early, Middle, and Late Archaic periods. The analysis of materials and results of all three field efforts are presented in this single volume. Geoarchaeological investigations show that four terraces (TO, Tl, T2, and T3) in the immediate site area accumulated from the Late Pleistocene through the Holocene. Five Stratigraphic Units (I-V) make up these terraces and overlap one another. The T2 terrace is composed of Stratigraphic Units IT, ill, and IV, while the Tl terrace consists mostly of Stratigraphic Units IV and V. Archaeological materials were discovered in situ within the Tl and T3 terraces and primarily within Stratigraphic Units ill and IV. Radiocarbon assays indicate that Stratigraphic Unit IV formed between at least 4000-2000 B.P., Stratigraphic Unit ill accumulated between approximately 11,500-4000 B.P., and Stratigraphic Unit IT was accreting at least 17,500 years ago. Too little evidence exists to determine the full time ranges of sediment accumulation, and whether significant temporal gaps exist between the sedimentation of these geological units. Archaeological excavations focused on three separate areas: A, B, and C. Area A is a new right-of-way east of the existing right-of-way. Excavations in this area defined a Late Archaic Montell component dating to approximately 2700 B.P. These materials include two burned rock features in situ within Unit IV on the scarp of the T2 terrace. This area probably was occupied by a small residential group during the Late Archaic period. Area B is east of Loop 1604 in the existing right-of-way and on the T2 terrace. Area B contains a Middle Archaic Nolan component in the upper portion of Stratigraphic Unit ill, below a Late Archaic burned rock midden with a central subsurface oven in Unit IV. Area C is in the existing right-of-way west of Loop 1604. Excavations in this area investigated the possibility of an intact Early Archaic occupation; however, no evidence of one was found. In Area B, the Nolan component consisted of lithic artifacts scattered among small burned rock features that probably served as hearths. This component is radiocarbon dated to approximately 4600 B.P. The Late Archaic burned rock midden was apparently used between 4000 B.P. and 2000 B.P. Subfeatures within the central oven indicate multiple cooking events. Ethnographic evidence suggests earth ovens contained food wrapped with insulating material over a layer of hot rocks heated by a coal bed. This was capped with dirt to seal the oven. When cooking was complete, the earth cap is removed to reach the food. CAR conducted earth-oven hot-rock experiments which indicated that local limestone could be used once or at the most twice. Local hot-rock cooking should generate a great deal of burned limestone debris. The framework ofthe feature at 41BX126 represents the cap and rock heating-element dumpings from separate cooking events as well as a few small intact burned rock features that served as ovens or hearths. At the base of the midden were a few depressions that may represent borrow pits used to obtain sediment for the central oven cap. Mixing of temporally distinct artifacts from the Nolan and later occupations occurs in and beyond the midden due to sediment excavation and transportation across the site, and redeposition of materials through erosion of materials off the framework.
30 citations
TL;DR: A reversible version of NC-PCA is defined, and it is proved by showing that a reversible two-counter machine, which has been known to be universal, can be simulated by a reversible NC- PCA.
Abstract: We introduce a new model of cellular automaton called a one-dimensional number-conserving partitioned cellular automaton (NC-PCA). An NC-PCA is a system such that a state of a cell is represented by a triple of non-negative integers, and the total (i. e., sum) of integers over the configuration is conserved throughout its evolving (computing) process. It can be thought as a kind of modelization of the physical conservation law of mass (particles) or energy. We also define a reversible version of NC-PCA, and prove that a reversible NC-PCA is computation-universal. It is proved by showing that a reversible two-counter machine, which has been known to be universal, can be simulated by a reversible NC-PCA.
30 citations
TL;DR: The Center for Archaeological Research (CAR) at The University of Texas at San Antonio (UTSA) conducted a Class III archaeology survey of 10,195 acres (4125 ha) within Twin Buttes Reservoir, a flood control and irrigation facility near the city of San Angelo in west-central Tom Green County, Texas as discussed by the authors.
Abstract: From December of 1998 through November of 1999, the Center for Archaeological Research (CAR), at The University of Texas at San Antonio (UTSA) conducted a Class III archaeology survey of 10,195 acres (4125 ha) within Twin Buttes Reservoir, a flood control and irrigation facility near the city of San Angelo in west-central Tom Green County, Texas. The 100 percent pedestrian survey, conducted for the Department of the Interior, Bureau of Reclamation (BOR), was primarily a section 110, of the National Historic Preservation Act (NHPA), effort. The survey was conducted in conjunction with repair of existing seepage at Twin Buttes Dam. The repair, conducted under the Safety of Dams program, involved the construction of several borrow pits. Since the Safety of Dams repair required BOR to inventory several areas of the reservoir lands under Section 106 of the NHPA, it was decided to expand the section 106 work, and do the entire Section 110 survey of the reservoir. CAR recorded 178 new archaeological sites, and revisited 21 previously recorded sites, within the reservoir. On these 199 sites, 19 historic components were identified, reflecting primarily farming and ranching activities. The prehistoric sites reflect occupation from the early Paleoindian period through the Late Prehistoric period. While recommendations regarding the eligibility of sites to the National Register of Historic Places (NRHP) were not required by the survey, based on the survey results CAR recommends that 13 of the 19 historic components have moderate or high research potential. Within the prehistoric data set, 48 sites have high research potential, 33 have moderate research potential, and 111 sites have limited research value.
24 citations
TL;DR: A partial answer to a question of Carlitz asking for a closed formula for the number of distinct representations of an integer in the Fibonacci base is given.
Abstract: We give a partial answer to a question of Carlitz asking for a closed formula for the number of distinct representations of an integer in the Fibonacci base.
21 citations
TL;DR: The first exponential lower bound for integer multiplication on the size of a nondeterministic nonoblivious read-once branching program model is proven and a lower bound method is presented.
Abstract: Branching programs are a well established computation model for Boolean functions, especially read-once branching programs have been studied intensively. In this paper the expressive power of nondeterministic read-once branching programs, more precisely the class of functions representable in polynomial size, is investigated. For that reason two restricted models of nondeterministic read-once branching programs are defined and a lower bound method is presented. Furthermore, the first exponential lower bound for integer multiplication on the size of a nondeterministic nonoblivious read-once branching program model is proven.
TL;DR: For example, the Adjutant General's Department of Texas conducted a self-sponsored Phase I cultural resources survey of Camp Swift in Bastrop County, Texas as discussed by the authors, which surveyed approximately 5,000 acres of the camp, approximately 1,000 of which had been previously surveyed.
Abstract: Beginning in November 1996 and continuing until July of 1997, the Adjutant General’s Department of Texas conducted a self-sponsored Phase I cultural resources survey of Camp Swift in Bastrop County, Texas. The project surveyed approximately 5,000 acres of the camp, approximately 1,000 of which had been previously surveyed. A total of 58 new archaeological sites were recorded, of which 26 were prehistoric, 24 were historic, and 8 had both prehistoric and historic components. In addition to these sites, 42 previously identified sites were revisited. In September 2000, the Center for Archaeological Research of the University of Texas at San Antonio completed shovel tests on two sites and acquired GPS data on 28 sites. At this time, a geomorphologist excavated a series of 12 backhoe trenches and—subsequently—a report on the geoarchaeology of Camp Swift was added to this report. An assessment of the 169 sites now known on Camp Swift found one site (41BP138, the Wine Cellar Site) eligible for inclusion in the National Register of Historic Places. A total of 106 sites are considered not eligible for inclusion in the National Register of Historic Places. Fifty-nine sites are considered potentially eligible, and should be tested to determine their eligibility. Three marked cemeteries are protected by state law.
TL;DR: Methods and results related to the notion of minimal forbidden words are applied to the fragment assembly problem and it is proved that, if w is a word randomly generated by a memoryless source with identical symbol probabilities, m(w) is logarithmic with respect to the size of w .
Abstract: In this paper methods and results related to the notion of minimal forbidden words are applied to the fragment assembly problem. The fragment assembly problem can be formulated, in its simplest form, as follows: reconstruct a word w from a given set I of substrings (fragments ) of a word w . We introduce an hypothesis involving the set of fragments I and the maximal length m(w) of the minimal forbidden factors of w . Such hypothesis allows us to reconstruct uniquely the word w from the set I in linear time. We prove also that, if w is a word randomly generated by a memoryless source with identical symbol probabilities, m(w) is logarithmic with respect to the size of w . This result shows that our reconstruction algorithm is suited to approach the above problem in several practical applications e.g. in the case of DNA sequences.
TL;DR: This paper surveys the area of Free Burnside Semigroups and gives priority to the mathematical treatment of the problem and does not stress too much neither motivation nor the historical aspects.
Abstract: This paper surveys the area of Free Burnside Semigroups. The theory of these semigroups, as is the case for groups, is far from being completely known. For semigroups, the most impressive results were obtained in the last 10 years. In this paper we give priority to the mathematical treatment of the problem and do not stress too much neither motivation nor the historical aspects. No proofs are presented in this paper, but we tried to give as many examples as was possible.
TL;DR: It is proved that MIN-MAX-SUBDAG problem, which is a generalization of MINLOP and requires to find a minimum cardinality maximal acyclic subdigraph of a given digraph, is, however, APX-hard.
Abstract: We study hardness of approximating several minimaximal and maximinimal NP-optimization problems related to the minimum linear ordering problem (MINLOP). MINLOP is to find a minimum weight acyclic tournament in a given arc-weighted complete digraph. MINLOP is APX-hard but its unweighted version is polynomial time solvable. We prove that MIN-MAX-SUBDAG problem, which is a generalization of MINLOP and requires to find a minimum cardinality maximal acyclic subdigraph of a given digraph, is, however, APX-hard. Using results of Hastad concerning hardness of approximating independence number of a graph we then prove similar results concerning MAX-MIN-VC (respectively, MAX-MIN-FVS) which requires to find a maximum cardinality minimal vertex cover in a given graph (respectively, a maximum cardinality minimal feedback vertex set in a given digraph). We also prove APX-hardness of these and several related problems on various degree bounded graphs and digraphs.
TL;DR: It is shown that a solution to the conjecture about the algebraic counterpart of the boolean closure of the polynomial closure would give a solution of the decidability of the levels 2 of the Straubing-Therien hierarchy and of the dot-depth hierarchy.
Abstract: In a previous paper, the authors studied the polynomial closure of a variety of languages and gave an algebraic counterpart, in terms of Mal'cev products, of this operation. They also formulated a conjecture about the algebraic counterpart of the boolean closure of the polynomial closure --- this operation corresponds to passing to the upper level in any concatenation hierarchy ---. Although this conjecture is probably true in some particular cases, we give a counterexample in the general case. Another counterexample, of a different nature, was independently given recently by Steinberg. Taking these two counterexamples into account, we propose a modified version of our conjecture. We show in particular that a solution to our new conjecture would give a solution of the decidability of the levels 2 of the Straubing-Therien hierarchy and of the dot-depth hierarchy. Consequences for the other levels are also discussed.
TL;DR: A more probabilistic view is taken which leads to a limit theorem for the random number of steps required by the algorithm and also helps to explain the limiting logarithmic periodicity as a simple discretization phenomenon.
Abstract: We investigate the number of iterations needed by an ad- dition algorithm due to Burks et al. if the input is random. Several authors have obtained results on the average case behaviour, mainly using analytic techniques based on generating functions. Here we take a more probabilistic view which leads to a limit theorem for the distri- bution of the random number of steps required by the algorithm and also helps to explain the limiting logarithmic periodicity as a simple discretization phenomenon.
TL;DR: The depth hierarchy results for monotones of Raz and McKenzie are extended to the case of monotone circuits of semi-unbounded fan-in and it follows that the inclusions NC i ⊆ SAC i⊆ AC i are proper in the monot one setting.
Abstract: The depth hierarchy results for monotone circuits of Raz and McKenzie [5] are extended to the case of monotone circuits of semi-unbounded fan-in. It follows that the inclusions NC i ⊆ SAC i ⊆ AC i are proper in the monotone setting, for every i ≥ 1.
TL;DR: The work performed by the Center for Archaeological Research (CAR) at The University of Texas San Antonio (UTSA) for City Public Service (CPS) was carried out under Texas Historical Commission (THC) Permit Number: 2020, and the work was conducted at each of the four historical San Antonio missions.
Abstract: This report contains the results of archaeological work performed by the Center for Archaeological Research (CAR) at The University of Texas San Antonio (UTSA) for City Public Service (CPS). The archaeological investigation and monitoring for the Mission Trails Underground Conversion Project was carried out under Texas Historical Commission (THC) Permit Number: 2020, and the work was conducted at each of the four historical San Antonio missions which make up San Antonio Missions National Historical Park. The Mission Trails Underground Conversion Project was created to enhance and upgrade electrical and utility connections by replacing aboveground connections with underground connections at each ofthe four missions. Mission San Juan (41BX5)-In October of 1998, personnel from CAR began archaeological investigations at Mission San Juan Capistrano in advance of the proposed installation of underground utility lines for the Mission Trails Underground Conversion Project. The purpose of the investigation was to test for intact, buried cultural features in advance of trenching activities involved in the relocation of utility lines and connections. CAR archaeologists developed a plan regarding the area to be impacted which included ten 1 x 1-m excavations units and a series of twelve shovel tests along the proposed path of the utility trench. Excavation units uncovered evidence of existing buildings, wall foundations and Colonial-period flooring episodes, revealing new data west of the known structures and not previously accounted for. Further excavations are warranted to determine the nature of features such as a Colonial-period wall revealed near one of the excavation units. This material discovered by the archaeological investigations resulted in the altering of the projected utility trench alignment to avoid disturbing deposits. Further archaeological investigations are recommended for the newly revealed features. Mission San Jose (41BX3)In January of 1999, personnel from CAR began archaeological investigations at Mission San Jose y San Miguel de Aguayo in advance of the proposed installation of underground utility lines for the Mission Trails Underground Conversion Project. The purpose of the investigation was to test for intact, buried cultural features in advance of trenching activities involved in the relocation of utility lines and connections. CAR archaeologists conducted a series of shovel tests along the center-lines of the proposed utility trenches to identifY areas of possible impact to intact Spanish Colonial cultural materials. In addition to shovel testing, monitoring of the trenching was conducted in areas where the possibility of impacting cultural material was high. An early-twentieth century trash midden was encountered during monitoring of the trench where it paralleled the Service Drive in the northwest comer of the Mission compound. This material did not warrant altering the course of the trench, and no further archaeological work is recommended at this time. Mission Concepcion (41BX12)In January of 1999, personnel from CAR began archaeological investigations at Mission Nuestra Senora de la Purisima Concepcion as part of the Mission Trails Underground Conversion Project. A construction crew, while excavating a manhole designed to provide access to underground electrical utilities, had unearthed a large number of animal bones. After concluding a large feature had been unexpectedly impacted, CAR conducted test excavations to ascertain the nature of this feature. It was determined to be a section of an acequia which had been refilled during the Colonial period with construction debris and trash, including a large number of animal bones. Test units and the original manhole excavations allowed for a profile of the acequia to be constructed. This information combined with previous archaeological work and historical research, allowed a tentative proposal on the sequence of acequia construction and re-routing for the Concepcion mission. Monitoring of other underground work conducted in the area resulted in the discovery of a location of a Colonialperiod wall, southeast of the Visitors' Center, which may be a portion of the original south wall of the mission. It is recommended that if any further work is required, consideration should be given to testing and/or monitoring to reduce the risk of negative impact to historic remains. Mission Espada (41BX4)In July of 1999, personnel from CAR began archaeological investigations at Mission San Francisco de la Espada in advance of the proposed installation of underground utility lines for the Mission Trails Underground Conversion Project. From initial discussions, it was noted that the proximity of the proposed route of the underground utility trench could have an impact on the old compound walls of the mission and the path was altered to avoid any possible impact. A series of thirteen shovel tests were conducted in advance along the altered path of the proposed utility trench as it progressed from the southwest comer of the mission compound across the dry irrigation ditch or acequia to the northwest. Monitoring of the trenching activities followed with no significant deposits being exposed. No further work is recommended within the project area, but if future construction is to occur in the area between the utility trench and the Church at Mission Espada, monitoring should then be considered.
TL;DR: It is proved that graph products of automatic monoids of finite geometric type are still automatic and a similar result for prefix-automatic monoids is established.
Abstract: The graph product is an operator mixing direct and free products. It is already known that free
products and direct products of automatic monoids are automatic. The main aim of this paper is to
prove that graph products of automatic monoids of finite geometric type are still automatic.
A similar result for prefix-automatic monoids is established.
TL;DR: This paper shows that this semantics provides a smooth interpretation for subtyping, a central notion in object-oriented programming, and shows that different characterisations of behavioural subtyped found in the literature can conveniently be expressed in coalgebraic terms.
Abstract: Coalgebras have been proposed as formal basis for the semantics of objects in the sense of object-oriented programming. This paper shows that this semantics provides a smooth interpretation for subtyping, a central notion in object-oriented programming. We show that different characterisations of behavioural subtyping found in the literature can conveniently be expressed in coalgebraic terms. We also investigate the subtle difference between behavioural subtyping and refinement.
TL;DR: Given an integer k ≥ 2, it is proved that a binary morphism is k -power-free if and only if it is k +1 up to k 2 and this bound becomes linear for primitive morphisms.
Abstract: A morphism f is k -power-free if and only if f(w) is k -power-free whenever w is a k -power-free word. A morphism f is k -power-free up to m if and only if f(w) is k -power-free whenever w is a k -power-free word of length at most m . Given an integer k ≥ 2, we prove that a binary morphism is k -power-free if and only if it is k -power-free up to k 2 . This bound becomes linear for primitive morphisms: a binary primitive morphism is k -power-free if and only if it is k -power-free up to 2k+1
TL;DR: The average-case analysis of an important parameter of this tree-structure, i.e. the stack-size, is obtained and it is established that, when the source emits independent symbols, the optimal ordering arises when the most probable symbol is the last one in this order.
Abstract: Digital trees or tries are a general purpose flexible data structure that implements dictionaries built on words. The present paper is focussed on the average-case analysis of an important parameter of this tree-structure, i.e. , the stack-size. The stack-size of a tree is the memory needed by a storage-optimal preorder traversal. The analysis is carried out under a general model in which words are produced by a source (in the information-theoretic sense) that emits symbols. Under some natural assumptions that encompass all commonly used data models (and more), we obtain a precise average-case and probabilistic analysis of stack-size. Furthermore, we study the dependency between the stack-size and the ordering on symbols in the alphabet: we establish that, when the source emits independent symbols, the optimal ordering arises when the most probable symbol is the last one in this order.
TL;DR: The class of languages of the form $L\cap R$, with a shuffle language L and a regular language R, contains non-semilinear languages and does not form a family of mildly context- sensitive languages.
Abstract: We investigate the complexity of languages described by some expressions
containing shuffle operator and intersection. We show that deciding whether
the shuffle of two words has a nonempty intersection with a regular set
(or fulfills some regular pattern) is NL-complete.
Furthermore we show that the class of languages of the form $L\cap R$
,
with a shuffle language L and a regular language R , contains
non-semilinear languages and does not form a family of mildly
context- sensitive languages.
TL;DR: It is said that two languages X and Y are conjugates if they satisfy the conjugacy equation XZ = ZY for some language Z, and all sets which are conjugal via a two-element biprex set Z are characterized.
Abstract: We say that two languages X and Y are conjugates if they satisfy the conjugacy equation XZ = ZY for some language Z. We study several problems associated with this equation. For example, we characterize all sets which are conjugated via a two-element biprex set Z, as well as all two-element sets which are conjugates. Mathematics Subject Classication. 68R15, 68Q70.
TL;DR: A modification of an algorithm for computing the Abelian kernel of a finite monoid obtained by the author in 1998 is given which is much more efficient in practice.
Abstract: Natural algorithms to compute rational expressions for recognizable languages, even those which work well in practice, may produce very long expressions. So, aiming towards the computation of the commutative image of a recognizable language, one should avoid passing through an expression produced this way. We modify here one of those algorithms in order to compute directly a semilinear expression for the commutative image of a recognizable language. We also give a second modification of the algorithm which allows the direct computation of the closure in the profinite topology of the commutative image. As an application, we give a modification of an algorithm for computing the Abelian kernel of a finite monoid obtained by the author in 1998 which is much more efficient in practice.
TL;DR: This work argues that in practice the restrictions that these constraints impose on the occurrences of null values in relations are too strict, and justifies a generalisation of the said constraints wherein key families are used, which are collections of attribute sets of a relation schema, rather than keys.
Abstract: Entity and referential integrity are the most fundamental constraints that any relational database should satisfy. We re-examine these fundamental constraints in the context of incomplete relations, which may have null values of the types "value exists but is unknown" and "value does not exist" . We argue that in practice the restrictions that these constraints impose on the occurrences of null values in relations are too strict. We justify a generalisation of the said constraints wherein we use key families, which are collections of attribute sets of a relation schema, rather than keys, and foreign key families which are collections of pairs of attribute sets of two relation schemas, rather than foreign keys. Intuitively, a key family is satisfied in an incomplete relation if each one of its tuples is uniquely identifiable on the union of the attribute sets of the key family, in all possible worlds of the incomplete relation, and, in addition, is distinguishable from all the other tuples in the incomplete relation by its nonnull values on some element in the key family. Our proposal can be viewed as an extension of Thalheim's key set, which only deals with null values of type "value exists but is unknown" . The intuition behind the satisfaction of a foreign key family in an incomplete database is that each pair of attribute sets in the foreign key family takes the foreign key attribute values over F i of a tuple in one incomplete relation referencing the key attribute values over K i of a tuple in another incomplete relation. Such referencing is defined only in the case when the foreign key attribute values do not have any null values of the type "value does not exist" ; we insist that the referencing be defined for at least one such pair. We also investigate some combinatorial properties of key families, and show that they are comparable to the standard combinatorial properties of keys.
TL;DR: It is proved that a word of length n from a finitely ambiguous context-free language can be generated at random under uniform distribution in O (n 2 log n ) time by a probabilistic random access machine assuming a logarithmic cost criterion.
Abstract: We prove that a word of length n from a finitely ambiguous context-free language can be generated at random under uniform distribution in O (n 2 log n ) time by a probabilistic random access machine assuming a logarithmic cost criterion. We also show that the same problem can be solved in polynomial time for every language accepted by a polynomial time 1 -NAuxPDA with polynomially bounded ambiguity.
TL;DR: It is proved that for each positive integer n, the finite commutative language En = c (a 1 a 2 ...an ) possesses a test set of size at most 5n.
Abstract: We prove that for each positive integer n, the finite commutative language En = c (a 1 a 2 ...an ) possesses a test set of size at most 5n. Moreover, it is shown that each test set for E n has at least n -1 elements. The result is then generalized to commutative languages L containing a word w such that (i) alph(w ) = alph}(L ); and (ii) each symbol a ∈ alph}(L ) occurs at least twice in w if it occurs at least twice in some word of L : each such L possesses a test set of size 11n , where n = Card(alph(L )). The considerations rest on the analysis of some basic types of word equations.
TL;DR: In this article, the authors present a survey of natural and historic factors of site disturbance in the context of archeological and gearchaeological sites, as well as the results of Magnetic Sediment Susceptibility Testing (MST).
Abstract: .............................................................................................................................................................. i Figures .............................................................................................................................................................. iii Tables .............................................................................................................................................................. iv Acknowledgments .............................................................................................................................................. v Chapter 1: Introduction Introduction .................................................................................................................................................. 1 Report Organization ..................................................................................................................................... 1 Chapter 2: Environmental Setting Environmental Setting .................................................................................................................................. 3 Chapter 3: Cultural Setting Introduction .................................................................................................................................................. 5 Cultural Setting ............................................................................................................................................ 6 Chapter 4: Archaeological Background Archaeological Background ....................................................................................................................... 11 Chapter 5: Geoarchaeology Introduction ................................................................................................................................................ 12 Chapter 6: Methodology Introduction ................................................................................................................................................ 19 Chapter 7: Results Introduction ................................................................................................................................................ 23 Natural Factors of Site Disturbance ........................................................................................................... 23 Historic Factors of Site Disturbance .......................................................................................................... 24 Chapter 8: Recommendations Recommendations ...................................................................................................................................... 95 References Cited ............................................................................................................................................... 99 Appendix A: Soil Profile Descriptions .......................................................................................................................... 106 Appendix B: Magnetic Sediment Susceptibility Testing ............................................................................................... 116 Camp Maxey III: Supplement Supplement ................................................................................................................................................... *