Showing papers in "Acta Informatica in 1994"
IBM1
TL;DR: It is concluded that B-trees can be used advantageously in a multi-user environment because the solution presented here uses simple locking protocols which can be tuned to specific requirements.
Abstract: Concurrent operations on B-trees pose the problem of insuring that each operation can be carried out without interfering with other operations being performed simultaneously by other users. This problem can become critical if these structures are being used to support access paths, like indexes, to data base systems. In this case, serializing access to one of these indexes can create an unacceptable bottleneck for the entire system. Thus, there is a need for locking protocols that can assure integrity for each access while at the same time providing a maximum possible degree of concurrency. Another feature required from these protocols is that they be deadlock free, since the cost to resolve a deadlock may be high.
Recently, there has been some questioning on whether B-tree structures can support concurrent operations. In this paper, we examine the problem of concurrent access to B-trees. We present a deadlock free solution which can be tuned to specific requirements. An analysis is presented which allows the selection of parameters so as to satisfy these requirements.
The solution presented here uses simple locking protocols. Thus, we conclude that B-trees can be used advantageously in a multi-user environment.
405 citations
TL;DR: This work combines the ideas of remote attribute access and inheritance to define “attribution modules” that can be reused in a variety of applications and shows how to define reusable modules for name analysis that embody different scope rules.
Abstract: An attribute grammar is a declarative specification of dependence among computations carried out at the nodes of a tree. Attribute grammars have proven remarkably difficult to decompose into logical fragments. As a result, they have not yet been accepted as a viable specification technique. By combining the ideas of remote attribute access and inheritance, we have been able to define “attribution modules” that can be reused in a variety of applications. As an example, we show how to define reusable modules for name analysis that embody different scope rules.
117 citations
TL;DR: It is shown that the languages over a one-letter alphabet generated by context-free matrix grammars are always regular and a decision procedure is given for the question of whether a context- free matrix language is finite.
Abstract: This paper shows that the languages over a one-letter alphabet generated by context-free matrix grammars are always regular. Moreover we give a decision procedure for the question of whether a context-free matrix language is finite. Hereby we strengthen a result of [Mk 92] and settle a number of open questions in [DP 89]. Both results are obtained by a reduction to Petri net problems.
93 citations
TL;DR: In this article, a comprehensive description of a typed version of the LPF logic known as LPF is given, which is basic to formal specification and verified design in the software development method VDM and can be reconstructed classically by embedding into classical infinitary logic.
Abstract: This paper gives a comprehensive description of a typed version of the logic known as LPF. This logic is basic to formal specification and verified design in the software development method VDM. If appropriately extended to deal with recursively defined functions, the data types used in VDM, etc., it gives the VDM notation and its associated rules of reasoning. The paper provides an overview of the needed extensions and examines some of them in detail. It is shown how this nonclassical logic-and the extensions-can be reconstructed classically by embeddings into classical infinitary logic.
75 citations
TL;DR: In this article, the authors provide a precise analysis of the standard top-down recursive mergesort algorithm, in the average case, as well as in the worst and best cases.
Abstract: Mellin transforms and Dirichlet series are useful in quantifying periodicity phenomena present in recursive divide-and-conquer algorithms. This note illustrates the techniques by providing a precise analysis of the standard topdown recursive mergesort algorithm, in the average case, as well as in the worst and best cases. It also derives the variance and shows that the cost of mergesort has a Gaussian limiting distribution. The approach is applicable to a number of divide-and-conquer recurrences. Many algorithms are based on a recursive divide-and-conquer strategy of splitting a problem into two subproblems of equal or almost equal size, separately solving the subproblems, and then knitting their solutions together to find the solution to the original problem
64 citations
TL;DR: The path length of random skip lists is analyzed asymptotically and a precise asymPTotic result on the variance is derived, being of ordern2 (which is in contrast to tries under the symmetric Bernoulli model, where it is only of order n).
Abstract: The skip list is a recently introduced data structure that may be seen as an alternative to (digital) tries. In the present paper we analyze the path length of random skip lists asymptotically, i.e. we study the cumulated successful search costs. In particular we derive a precise asymptotic result on the variance, being of ordern 2 (which is in contrast to tries under the symmetric Bernoulli model, where it is only of ordern). We also intend to present some sort of technical toolkit for the skilful manipulation and asymptotic evaluation of generating functions that appear in this context.
54 citations
TL;DR: A parallel machine scheduling problem is considered in which each job has a processing time and a delivery time and several heuristics using list scheduling as a subroutine are proposed and a tight worst-case analysis is given.
Abstract: A parallel machine scheduling problem is considered in which each job has a processing time and a delivery time. The objective is to find a schedule which minimizes the time by which all jobs are delivered. For a single machine this problem is easily solved in polynomial time, form≥2 machines it becomes NP-hard. Several heuristics using list scheduling as a subroutine are proposed and a tight worst-case analysis is given. The best one of our heuristics has a worst-case performance guarantee of 2−2/(m+1). For the on-line case we give a heuristic with the (best possible) worst-case performance of two.
53 citations
TL;DR: A constructiion is described which, given a queryQ under the output-restricted unlimited interpretation, yields a domain independent queryQ′, with length no more than exponential in the length ofQ, such that Q andQ′ (under their respective semantics) express the same function.
Abstract: Several alternative semantics (or interpretations) of the relational (domain) calculus are studied here. It is shown that they all have the same expressive power, i.e., the selection of any of the semantics neither gains nor loses expressive power. Since the domain is potentially infinite, the answer to a relational calculus query is sometimes infinite (and hence not a relation). The following approaches which guarantee the finiteness of answers to queries are studied here:output-restricted unlimited interpretation, domain independent queries, output-restricted finite andcountable invention, andlimited interpretation. Of particular interest is the output-restricted unlimited interpretation—although the output is restricted to the active domain of the input and query, the quantified variables range over the infinite underlying domain. While this is close to the intuitive interpretation given to calculus formulas, the naive approach to evaluating queries under this semantics calls for the impossible task of examining infinitely many values. We describe here a constructiion which, given a queryQ under the output-restricted unlimited interpretation, yields a domain independent queryQ′, with length no more than exponential in the length ofQ, such thatQ andQ′ (under their respective semantics) express the same function.
48 citations
TL;DR: This work deals with the generation of code selectors in compiler backends using the theory of regular tree grammars and finite tree automata to construct algorithms that generalize and improve existing methods.
Abstract: We deal with the generation of code selectors in compiler backends. The fundamental concepts are systematically derived from the theory of regular tree grammars and finite tree automata. We use this general approach to construct algorithms that generalize and improve existing methods.
44 citations
TL;DR: A new transition system based on local and global causes based on causal bisimulation and location equivalence is introduced, parameterized by a functionf which evaluates the information on causes provided by the transitions.
Abstract: For CCS [15] several noninterleaving semantics have been proposed among which causal bisimulation [9] and location equivalence [6] play a central role. To unify these two approaches this paper introduces a new transition system based onlocal andglobal causes. Bisimulation equivalence is parameterized by a functionf which evaluates the information on causes provided by the transitions. Appropriate instantiations off yield characterizations of causal bisimulations and location equivalence.
41 citations
TL;DR: It is proved that the family ℱ of all languages which are closed with respect to a right-monotone well quasi-order on a finitely generated free monoid is closed under rational operations, intersection, inverse morphisms and direct non-erasing morphisms, which implies thatℱ is open under faithful rational transductions.
Abstract: An extension of Myhill's theorem of automata theory, due to Ehrenfeucht et al. [4] shows that a subsetX of a semigroupsS is recognizable if and only ifX is closed with respect to a monotone well quasi-order onS. In this paper we prove that a similar extension of Nerode's theorem is not possible by showing that there exist non-regular languages on a binary alphabet which are closed with respect to a right-monotone well quasi-order. We give then some additional conditions under which a setX S closed with respect to a right-monotone well quasi-order becomes recognizable. We prove the following main proposition: A subsetX ofS is recognizable if and only ifX is closed with respect to two well quasi-orders<=1 and<=2 which are right-monotone and left-monotone, respectively. Some corollaries and applications are given. Moreover, we consider the family ℱ of all languages which are closed with respect to a right-monotone well quasi-order on a finitely generated free monoid. We prove that ℱ is closed under rational operations, intersection, inverse morphisms and direct non-erasing morphisms. This implies that ℱ is closed under faithful rational transductions. Finally we prove that the languages in ℱ satisfy a suitable ‘pumping’ lemma and that ℱ contains languages which are not recursively enumerable.
TL;DR: For everyTCSP processP, it is obtained that its operational meaningO(P) and the interleaving behaviourO( M∥3P∢3) which is derived from the event structureM∦3P ∥3 associated withP are bisimilar.
Abstract: The relation between an operational interleaving semantics for TSCP based on a transition system and a compositional true concurrency semantics based on event structures is studied. In particular we extend the consistency result of U. Goltz and R. Loogen [Ann. Soc. Math. Pol., Ser. IV, Fundam. Inf. 14, 39-73 (1991; Zbl 0717.68028)] for TCSP processes without recursion to the general case. Thus, we obtain for every TCSP process P that its operational meaning O(P) and the interleaving behaviour O(M[[P]]) which is derived from the event structure M[[P]] associated with P are bisimilar. (aus: Zentralblatt MATH)
TL;DR: This paper presents an aminimum space algorithm that sortsstably a multiset in asymptoticallyOptimal worst-case time and develops linear-time in-place algorithms for the following problems, which have interest of their own.
Abstract: We consider the problem of sorting a multiset of sizen containingm distinct elements, where theith distinct element appearsn i times. Under the assumption that our model of computation allows only the operations of comparing elements and moving elements in the memory,Ω(n logn ? ? i=1 m n i logn i +n) is known to be a lower bound for the computational complexity of the sorting problem. In this paper we present aminimum space algorithm that sortsstably a multiset in asymptoticallyOptimal worst-case time. A Quicksort type approach is used, where at each recursive step the median is chosen as the partitioning element. To obtain a stable minimum space implementation, we develop linear-time in-place algorithms for the following problems, which have interest of their own:
Stable unpartitioning: Assume that ann-element arrayA is stably partitioned into two subarraysA 0 andA 1. The problem is to recoverA from its constitutentsA 0 andA 1. The information available is the partitioning element used and a bit array of sizen indicating whether an element ofA 0 orA 1 was originally in the corresponding position ofA.
Stable selection: The task is to find thekth smallest element in a multiset ofn elements such that the relative order of identical elements is retained.
TL;DR: A proper generalization of McNaughton's Theorem from infinite words to infinite traces is given and it is obtained that every closed word language is accepted by someI-diamond deterministic Muller automaton.
Abstract: This paper shows the equivalence between the family of recognizable languages over infinite traces and the family of languages which are recognized by deterministic asynchronous cellular Muller automata. We thus give a proper generalization of McNaughton's Theorem from infinite words to infinite traces. Thereby we solve one of the main open problems in this field. As a special case we obtain that every closed (w.r.t. the independence relation) word language is accepted by someI-diamond deterministic Muller automaton.
TL;DR: The relationships of CPT with other models of Grammars cooperating together and with various kinds of controlled grammars are established and some open problems from [6] are solved and alternative proofs for some results are provided.
Abstract: We consider sets of grammars (calledteams) which process strings by cooperating together; a single derivation step in a team is done in such a way that each grammar in the set rewrites a symbol in the string. A cooperating grammar system with prescribed teams (CPT) consists of a finite number of teams. In a maximal rewriting mode, a team in a CPT can take a string for rewriting whenever it can make a derivation step on it; it keeps it and rewrites as long as it can, and once a string is obtained that cannot be rewritten by the team anymore it is returned and becomes available to all other teams. In this paper we investigate the power of CPT in the maximal and other rewriting modes. We establish the relationships of CPT with other models of grammars cooperating together and with various kinds of controlled grammars. We also solve some open problems from [6] and provide alternative proofs for some results from [6].
TL;DR: A new formal model for the concept of syntax-directed semantics, called macro attributed tree transducer, is introduced, based on (noncircular) attributedTree transducers and on macro tree transducers.
Abstract: In this paper we introduce a new formal model for the concept of syntax-directed semantics, called macro attributed tree transducer (for skort: mat tree transducer). This model is based on (noncircular) attributed tree transducers and on macro tree transducers. In the first type of transducer, semantic values are computed by means of meaning names called synthesized attributes, and by means of context names called inherited attributes. Both, synthesized and inherited attributes represent basic semantic values. In the second type of transducer, semantic values are computed by meaning names only which are called states. However, in order to have a means of handling context information, states represent functions over semantic values
TL;DR: A method based on geometrical tools to map problems onto regular and synchronous processor arrays defined by systems of affine recurrence equations by extracting data dependencies in terms of two classes of vectors: the utilization vectors and the dependence vectors.
Abstract: We propose a method based on geometrical tools to map problems onto regular and synchronous processor arrays. The problems we consider are defined by systems of affine recurrence equations (SARE). From such a problem specification we extract the data dependencies in terms of two classes of vectors: the utilization vectors and the dependence vectors. We use these vectors to express constraints on the timing or the allocation functions. We differentiate two classes of constraints. The causal ones are intrinsic timing constraints induced by the system of equations defining the problem. A given choice of target architecture may impose new constraints on the timing or the allocation. We call them the architecture-related constraints. We use these constraints to determine first an affine timing function and next an allocation by projection. We finally illustrate the method with three examples: the matrix multiplication, the recursive convolution and the LLt Cholesky factorization.
TL;DR: The apex graph grammars generate precisely the context-free graph languages of bounded degree, independently of whether one considers hyperedge replacement systems or (boundary or confluent) NLC or edNCE graph Grammars.
Abstract: The apex graph grammars generate precisely the context-free graph languages of bounded degree, independently of whether one considers hyperedge replacement systems or (boundary or confluent) NLC or edNCE graph grammars. The main feature of apex graph grammars is that nodes cannot be "passed" from nonterminal to nonterminal. The proof is based on a normal form result for arbitrary hyperedge replacement systems that forbids "passing chains". This generalizes Greibach Normal Form.
TL;DR: Information theoretic approximations for the M/G/1 queue with retrials are presented according to the available information about the service time probability density and the steady-state distribution of the system state.
Abstract: In this paper we present information theoretic approximations for theM/G/1 queue with retrials. Various approximations for this model are obtained according to the available information about the service time probability density and the steady-state distribution of the system state. The results are well-suited for numerical computation.
TL;DR: A generalization of binary search trees and binary split trees is developed that takes advantage of two-way key comparisons and can improve search cost by up to 50% over the optimal binary search tree.
Abstract: A generalization of binary search trees and binary split trees is developed that takes advantage of two-way key comparisons: the two-way comparison tree. The two-way comparison tree has little use for dynamic situations but is an improvement over the optimal binary search tree and the optimal binary split tree for static data sets. AnO(n) time and space algorithm is presented for constructing an optimal two-way comparison tree when access probabilities are equal, and an exact formula for the optimal cost is developed. The construction of the optimal two-way comparison tree for unequal access frequencies, both successful and unsuccessful, is computable inO(n 5) time andO(n 3) space using algorithms similar to those for the optimal binary split tree. The optimal two-way comparison tree can improve search cost by up to 50% over the optimal binary search tree.
TL;DR: A categorial semantic domain for objects is presented in order to clarify both aggregation and specialization and shows the second category to be adequate for explaining specialization with side effects (by relaxing the frame constraint).
Abstract: A categorial semantic domain for objects is presented in order to clarify both aggregation and specialization. Three kinds of specialization are discussed: (1) subtyping (specialization with no side effects and no non-monotonic overriding); (2) monotonic specialization (possibly with side effects but still only with monotonic overriding); and (3) non-monotonic specialization (possibly with side effects and non-monotonic overriding). A sequence of three categories of objects differing only in the morphisms is presented. The first one is used to explain object aggregation (respecting locality through a frame constraint) and the strictest form of specialization (subtyping). The second category is shown to be adequate for explaining specialization with side effects (by relaxing the frame constraint). Finally, the third category supports also non-monotonic overriding, by adopting as morphisms suitable partial morphisms of the second one. All these categories are complete and cocomplete. Colimits are used for explaining the semantics of aggregation and multiple inheritance.
TL;DR: Context-free grammars for texts are introduced and their basic properties are investigated and it is found that each text has its own individual structure, which leads to the notion of ashapely context-free text grammar.
Abstract: A text is a tripleτ=(λ,ρ1,ρ2) such that λ is a labeling function, andρ1 andρ2 are linear orders on the domain of λ; hence τ may be seen as a word (λ,ρ1) together with an additional linear orderρ2 on the domain of λ. The orderρ2 is used to give to the word (λ,ρ1) itsindividual hierarchical representation (syntactic structure) which may be a tree but it may be also more general than a tree. In this paper we introducecontext-free grammars for texts and investigate their basic properties. Since each text has its own individual structure, the role of such a grammar should be that of a definition of a pattern common to all individual texts. This leads to the notion of ashapely context-free text grammar also investigated in this paper.
TL;DR: This paper shows that the algebra Pℛ of primitive recursive functions over the natural numbers has a recursive equational specification under second order initial algebra semantics, and it follows that higher orderinitial algebra specifications are strictly more powerful than first order initialgebra specifications.
Abstract: Theoretical results on the scope and limits of first order algebraic specifications can be used to show that certain natural algebras have no recursively enumerable equational specification under first order initial algebra semantics. A well known example is the algebraP? of primitive recursive functions over the natural numbers. In this paper we show thatP? has a recursive equational specification under second order initial algebra semantics. It follows that higher order initial algebra specifications are strictly more powerful than first order initial algebra specifications.
TL;DR: This paper focuses on observability issues in the framework of loose algebraic specifications by comparing various behavioural approaches developed so far and pointing out their respective advantages and limitations.
Abstract: This paper focuses on observability issues in the framework of loose algebraic specifications. The main purpose of observability is to extend the model class of some given algebraic specification in order to consider not only the algebras that satisfy the axioms of the specification in order to consider not only the algebras that satisfy the axioms of the specification, but as well other ones, provided that the differences between the properties satisfied by these algebras and the properties required by the specification (i.e., the axioms) are not “observable”. We compare various behavioural approaches developed so far. We point out their respective advantages and limitations. Expressive power is our main criterion for the discussion.
TL;DR: It is shown that the familyK-REC of forests supporting recognizable formal power series on trees is a sheaf and so is the family OCF of behaviors of one counter treeautomata.
Abstract: An alphabetic cone is a family of forests stable under alphabetic tree transductions, whereas we call REC-closed each family of forests closed under the operations of union, top-catenation,a-product anda-star; the sheaves are families having both the above properties.
TL;DR: It is proved that mat tree transducers are more powerful than both, attributed tree Transducers and macro tree transducer, and that the addition of inherited attributes does not increase the computational power of macroTree transducers.
Abstract: In this paper we introduce a new formal model for the concept of syntaxdirected semantics, calledmacro attributed tree transducer (for short: mat tree transducer). This model is based on (noncircular) attributed tree transducers and on macro tree transducers. In the first type of transducer, semantic values are computed by means of meaning names called synthesized attributes, and by means of context names called inherited attributes. Both, synthesized and inherited attributes represent basic semantic values. In the second type of transducer, semantic values are computed by meaning names only which are called states. However, in order to have a means of handling context information, states represent functions over semantic values. The new model integrates attributed tree transducers and macro tree transducers by allowing both, meaning names and context names to represent functions over semantic values. In analogy to the terminology of attributed tree transducers, we call such meaning names and context names also synthesized functions and inherited functions, respectively.
We present an inductive characterization of the tree transformation computed by an mat tree transducer. We prove that mat tree transducers are more powerful than both, attributed tree transducers and macro tree transducers. We characterize mat tree transducers by the two-fold composition of attributed tree transducers. This characterization has three consequences: (1) the height of output trees of mat tree transducers is bounded exponentially in the size of the input tree, (2) the composition hierarchy of mat tree transducers is strict, and (3) mat tree transducers are closed under right-composition with top-down tree transducers, but not under left-composition. Moreover, we prove that the addition of inherited attributes does not increase the computational power of macro tree transducers.
TL;DR: A semantic method based on a non-standard CCS operational semantics that is able to decide the finiteness of a CCS term in a larger number of cases than those captured by known syntactic criteria.
Abstract: We present a semantic method to check the finiteness of CCS terms. The method is interpretative, i.e. it is based on a non-standard CCS operational semantics. According to this semantics it is always possible, given a processp, to build a finite state transition system which, if a condition holds, is a finite representation ofp; otherwise it is a suitable approximation of its semantic behaviour. The method is able to decide the finiteness of a CCS term in a larger number of cases than those captured by known syntactic criteria.
TL;DR: Several natural problems, involving Boolean satisfiability, graph colouring and Hamiltonian circuits, are complete forf (n)-NP, which is shown to be a well-known NP-complete problem.
Abstract: We consider languages in NP whose certificate size is bounded by a fixed, slowly growing function (sayf (n)) of the input size The classesf (n)-NP, which are related to classes of Kintala and Fischer, are defined in order to classify such languages We show that several natural problems, involving Boolean satisfiability, graph colouring and Hamiltonian circuits, are complete forf (n)-NP Each of our problems is obtained by taking a known NP-complete problem and introducing an ingredient we callforcing, whereby a partial structure is enlarged by a sequence of local improvements As special cases of these results we obtain some new logspace completeness results for P
TL;DR: A characterization of NP in terms of communication-bounded multihead synchronized alternating finite automata, namely, NP = ⋃k≥1L(SAFA(k-heads,nk -com)).
Abstract: We continue the study of communication-bounded synchronized alternating finite automata (SAFA), first considered by Hromkovia? et al. We show that to accept a nonregular language, an SAFA needs to generate at least Ω(log logn) communication symbols infinitely often; furthermore, a synchronized alternating finite automaton without nondeterminism (SUFA) needs to generate at leastΩ(log logn) communication symbols infinitely often for some constantk?1. We also show that these bounds are tight.
Next, we establish dense hierarchies of these machines on the function bounding the number of communication symbols. Finally, we give a characterization of NP in terms of communication-bounded multihead synchronized alternating finite automata, namely, NP = ? k?1 L(SAFA(k-heads,n k -com)). This result recasts the relationships between P, NP, and PSPACE in terms of multihead synchronized alternating finite automata.
TL;DR: In this paper, an extension of the turtle geometry interpretation is introduced that enables L-systems to generate gray-tone images, and it is shown that every Weighted Finite Automaton can be simulated step-by-step by a DOL-system.
Abstract: Image generation with DOL-systems is discussed. It is shown that, if either the vector or the turtle geometry interpretation is used, DOL-systems can produce step-by-step all images that can be generated by regular languages (or by equivalent Iterative Matrix Homomorphisms of Shallit and Stolfi). An extension of turtle geometry interpretation is introduced that enables L-systems to generate gray-tone images. It is shown that with our extension every Weighted Finite Automaton can be simulated step-by-step by a DOL-system.