Showing papers in "International Journal of Foundations of Computer Science in 2013"
TL;DR: The language stream (Un(a, b, c) | n ≥ 3) is defined by the deterministic finite automaton, where a performs a cyclic permutation of the n states, b transposes states 0 and 1, and c maps state n − 1 to state 0.
Abstract: Sequences (Ln | n ≥ k), called streams, of regular languages Ln are considered, where k is some small positive integer, n is the state complexity of Ln, and the languages in a stream differ only in the parameter n, but otherwise, have the same properties The following measures of complexity are proposed for any stream: (1) the state complexity n of Ln, that is, the number of left quotients of Ln (used as a reference); (2) the state complexities of the left quotients of Ln; (3) the number of atoms of Ln; (4) the state complexities of the atoms of Ln; (5) the size of the syntactic semigroup of Ln; and the state complexities of the following operations: (6) the reverse of Ln; (7) the star of Ln; (8) union, intersection, difference and symmetric difference of Lm and Ln; and (9) the concatenation of Lm and Ln A stream that has the highest possible complexity with respect to these measures is then viewed as a most complex stream The language stream (Un(a, b, c) | n ≥ 3) is defined by the deterministic finite automaton with state set {0, 1, … , n−1}, initial state 0, set {n−1} of final states, and input alphabet {a, b, c}, where a performs a cyclic permutation of the n states, b transposes states 0 and 1, and c maps state n − 1 to state 0 This stream achieves the highest possible complexities with the exception of boolean operations where m = n In the latter case, one can use Un(a, b, c) and Un(b, a, c), where the roles of a and b are interchanged in the second language In this sense, Un(a, b, c) is a universal witness This witness and its extensions also apply to a large number of combined regular operations
71 citations
TL;DR: This paper discusses research frontiers of membrane computing by presenting current open problems and research topics, together with the relevant background and motivation.
Abstract: This paper discusses research frontiers of membrane computing by presenting current open problems and research topics, together with the relevant background and motivation.
47 citations
TL;DR: This work investigates formal properties, mainly issues connected with propositional logic, of reaction systems introduced by Ehrenfeucht and Rozenberg with a particular focus on the most simple variant of the systems.
Abstract: We investigate formal properties, mainly issues connected with propositional logic, of reaction systems introduced by Ehrenfeucht and Rozenberg. We are concerned only with the most simple variant of the systems. Basic properties of propositional formulas are expressed in terms of reaction systems. This leads to NP-completeness (resp. co-NP-completeness) of many problems concerning reaction systems. Among such problems are: (i) deciding whether the function defined by the system is total, (ii) determining the inverse of the function, (iii) deciding whether state sequences always end with a loop. Propositional formulas with monotonic truth-functions yield a particularly simple representation in terms of reaction systems.
34 citations
TL;DR: Electronic version of an article published as International Journal of Foundations of Computer Science, 24(07), 2013, 1009–1027.
Abstract: Electronic version of an article published as International Journal of Foundations of Computer Science, 24(07), 2013, 1009–1027. http://dx.doi.org/10.1142/S0129054113400285 © World Scientific Publishing Company http://www.worldscientific.com/
21 citations
TL;DR: It is proved that the uniform recurrence of morphic sequences is decidable and the number of derived sequences of uniformly recurrent morphic Sequence is bounded, and it is obtained that uniformly recurrent Morphic sequences are primitive substitutive sequences.
Abstract: We prove that the uniform recurrence of morphic sequences is decidable. For this we show that the number of derived sequences of uniformly recurrent morphic sequences is bounded. As a corollary we obtain that uniformly recurrent morphic sequences are primitive substitutive sequences.
20 citations
TL;DR: In a wireless sensor network, the authors often require the deployment of new nodes to extend the lifetime of the network because some sensor nodes may be lost due to power exhaustion problem or they may be...
Abstract: In a wireless sensor network, we often require the deployment of new nodes to extend the lifetime of the network because some sensor nodes may be lost due to power exhaustion problem or they may be...
19 citations
TL;DR: The edit-distance between two strings is the smallest number of operations required to transform one string into the other.
Abstract: The edit-distance between two strings is the smallest number of operations required to transform one string into the other. The distance between languages L1 and L2 is the smallest edit-distance be...
18 citations
TL;DR: Two words u and v are k-abelian equivalent if they contain the same number of occurrences of each factor of length at most k and this leads to a hierarchy of equivalence relations on words which lie within this hierarchy.
Abstract: Two words u and v are k-abelian equivalent if they contain the same number of occurrences of each factor of length at most k. This leads to a hierarchy of equivalence relations on words which lie p...
17 citations
TL;DR: A new version of the so-called extension method that was used to prove quadratic upper bounds on the minimum length of reset words for various important classes of synchronizing automat... is described.
Abstract: We describe a new version of the so-called extension method that was used to prove quadratic upper bounds on the minimum length of reset words for various important classes of synchronizing automat...
16 citations
TL;DR: The class of languages captured by Constrained Automata that are unambiguous is shown to possess more closure properties than the provably weaker class captured by deterministic CA, and testing for regularity is added to this set of decidable problems.
Abstract: The class of languages captured by Constrained Automata (CA) that are unambiguous is shown to possess more closure properties than the provably weaker class captured by deterministic CA. Problems decidable for deterministic CA are nonetheless shown to remain decidable for unambiguous CA, and testing for regularity is added to this set of decidable problems. Unambiguous CA are then shown incomparable with deterministic reversal-bounded machines in terms of expressivity, and a deterministic model equivalent to unambiguous CA is identified.
15 citations
TL;DR: A technique for mechanically proving certain kinds of theorems in combinatorics on words, using finite automata and a software package for manipulating them is described, and the characteristic sequence of least periods of a k-automatic sequence is (effectively) k- automatic.
Abstract: We describe a technique for mechanically proving certain kinds of theorems in combinatorics on words, using finite automata and a software package for manipulating them. We illustrate our technique by applying it to (a) solve an open problem of Currie and Saari on the lengths of unbordered factors in the Thue-Morse sequence; (b) verify an old result of Prodinger and Urbanek on the regular paperfolding sequence; (c) find an explicit expression for the recurrence function for the Rudin-Shapiro sequence; and (d) improve the avoidance bound in Leech's squarefree sequence. We also introduce a new measure of infinite words called condensation and compute it for some famous sequences. We follow up on the study of Currie and Saari of least periods of infinite words. We show that the characteristic sequence of least periods of a k-automatic sequence is (effectively) k-automatic. We compute the least periods for several famous sequences. Many of our results were obtained by machine computations.
TL;DR: This paper shows the extension of a method presented for attacking the good parameters problem for Timed Automata with linear and affine dynamics for hybrid automata with Linear and Affine dynamics.
Abstract: Hybrid systems combine continuous and discrete behavior. Hybrid Automata are a powerful formalism for the modeling and verification of such systems. A common problem in hybrid system verification is the good parameters problem, which consists in identifying a set of parameter valuations which guarantee a certain behavior of a system. Recently, a method has been presented for attacking this problem for Timed Automata. In this paper, we show the extension of this methodology for hybrid automata with linear and affine dynamics. The method is demonstrated with a hybrid system benchmark from the literature.
TL;DR: For each odd n ≥ 5, a synchronizing Eulerian automaton with n states for which the minimum length of reset words is equal to .
Abstract: For each odd n ≥ 5 we present a synchronizing Eulerian automaton with n states for which the minimum length of reset words is equal to . We also discuss various connections between the reset threshold of a synchronizing automaton and a sequence of reachability properties in its underlying graph.
TL;DR: An algorithmic uniform method to measure the complexity of finitely refutable statements is proposed and is capable to classify Π2–statements, which cannot be evaluated with the original method.
Abstract: An algorithmic uniform method to measure the complexity of finitely refutable statements [6, 7, 9] was used to classify famous/interesting mathematical statements like Fermat's last theorem, the four colour theorem, and the Riemann hypothesis [8, 15, 16]. Working with inductive Turing machines of various orders [1] instead of classical computations, we propose a class of inductive complexity measures and inductive complexity classes for mathematical statements which generalise the previous method. In particular, the new method is capable to classify Π2–statements. As illustrations, we evaluate the inductive complexity of the Collatz and twin prime conjectures — statements which cannot be evaluated with the original method.
TL;DR: E-equivalence is introduced, which is a straightforward generalization of almost-Equivalence, which asks for ordinary equivalence up to a finite number of exceptions.
Abstract: We introduce E-equivalence, which is a straightforward generalization of almost-equivalence. While almost-equivalence asks for ordinary equivalence up to a finite number of exceptions, in E-equival...
TL;DR: An assume-guarantee system for network stability is derived and its efficiency to reason about any number of agents, any initial flow configuration, and any topology of bounded degree is shown.
Abstract: We investigate assume-guarantee reasoning for global specifications consisting of conjunctions of local specifications. We present a sound and complete assume-guarantee methodology that enables us to establish properties of a composite system by checking local specifications of its individual modules. We illustrate our approach with an example from the field of network congestion control, where different agents are responsible for controlling packet flow across a shared infrastructure. In this context we derive an assume-guarantee system for network stability and show its efficiency to reason about any number of agents, any initial flow configuration, and any topology of bounded degree.
TL;DR: Combinatorial Optimization is combined with Social Choice Theory when the goal is to decide on the quality of a spanning tree of an undirected graph.
Abstract: Combinatorial Optimization is combined with Social Choice Theory when the goal is to decide on the quality of a spanning tree of an undirected graph. Given individual preferences over the edges of ...
TL;DR: Existing and natural ways of combining the concept of homomorphic replacement with regular expressions fail to reach the expressive power of REGEX.
Abstract: We study different possibilities of combining the concept of homomorphic replacement with regular expressions in order to investigate the class of languages given by extended regular expressions with backreferences (REGEX). It is shown in which regard existing and natural ways to do this fail to reach the expressive power of REGEX. Furthermore, the complexity of the membership problem for REGEX with a bounded number of backreferences is considered.
TL;DR: This article put forward typed linear algebra as a candidate notation for such a unifying role, which emerges from regarding matrices as morphisms of suitable categories, and describes weighted automata as coalgebras in such categories.
Abstract: The evolution from non-deterministic to weighted automata represents a shift from qualitative to quantitative methods in computer science. The trend calls for a language able to reconcile quantitative reasoning with formal logic and set theory, which have for so many years supported qualitative reasoning. Such a lingua franca should be typed, polymorphic, diagrammatic, calculational and easy to blend with conventional notation. This paper puts forward typed linear algebra as a candidate notation for such a unifying role. This notation, which emerges from regarding matrices as morphisms of suitable categories, is put at work in describing weighted automata as coalgebras in such categories. Some attention is paid to the interface between the index-free (categorial) language of matrix algebra and the corresponding index-wise, set-theoretic notation.
TL;DR: In this paper, it was shown that the modulus function MODm of n variables can be computed by a threshold circuit C of energy e and size s = O(e(n/m)1/(e − 1)) for any integer e ≥ 2.
Abstract: We prove that the modulus function MODm of n variables can be computed by a threshold circuit C of energy e and size s = O(e(n/m)1/(e − 1)) for any integer e ≥ 2, where the energy e is defined to be the maximum number of gates outputting "1" over all inputs to C, and the size s to be the number of gates in C. Our upper bound on the size s almost matches the known lower bound s = Ω(e(n/m)1/e). We also consider an extreme case where threshold circuits have energy 1, and prove that such circuits need at least 2(n − m)/2 gates to compute MODm of n variables.
TL;DR: The Rh-connectivity of the (n, k)-star graph Sn,k is considered, denoted by κh(Sn,k), and it is determined that n+h(k−2)−1 for 2 ≤ k ≥ n−1 and 0 ≤ h ≤ n−k.
Abstract: This paper considers Rh-connectivity of the (n, k)-star graph Sn,k, denoted by κh(Sn,k). In this note, We determine κh(Sn,k) = n+h(k−2)−1 for 2 ≤ k ≤ n−1 and 0 ≤ h ≤ n−k. The results generalize the main result in proved by W. H. Yang et al. [Information Processing Letters, 110(2010), 1007–1011] for the R1-connectivity (κ1(Sn,k)) and R2-connectivity (κ2(Sn,k)).
TL;DR: It is shown that increasing the number of stacks of real-time pushdown automata can result in exponential improvement in the total amount of space usage for nonregular language recognition.
Abstract: We examine the minimum amount of memory for real-time, as opposed to one-way, computation accepting nonregular languages. We consider deterministic, nondeterministic and alternating machines working within strong, middle and weak space, and processing general or unary inputs. In most cases, we are able to show that the lower bounds for one-way machines remain tight in the real-time case. Memory lower bounds for nonregular acceptance on other devices are also addressed. It is shown that increasing the number of stacks of real-time pushdown automata can result in exponential improvement in the total amount of space usage for nonregular language recognition.
TL;DR: This work extends the notion of Parikh matrix of a word to a picture array and associates with it two kinds ofParikh matrices, called row ParikhMatrix and column Parikh Matrix, and obtains conditions that ensure M-ambiguity.
Abstract: Parikh matrix mapping or Parikh matrix of a word has been introduced in the literature to count the scattered subwords in the word. Several properties of a Parikh matrix have been extensively investigated. A picture array is a two-dimensional connected digitized rectangular array consisting of a finite number of pixels with each pixel in a cell having a label from a finite alphabet. Here we extend the notion of Parikh matrix of a word to a picture array and associate with it two kinds of Parikh matrices, called row Parikh matrix and column Parikh matrix. Two picture arrays A and B are defined to be M-equivalent if their row Parikh matrices are the same and their column Parikh matrices are the same. This enables to extend the notion of M-ambiguity to a picture array. In the binary and ternary cases, conditions that ensure M-ambiguity are then obtained.
TL;DR: This paper has implemented an elegant algorithm for EMS and compared it against 14 other algorithms in terms of sensitivity and specificity and results indicate that the new algorithm is very competitive in practice.
Abstract: Motifs are biologically significant patterns found in DNA/protein sequences. Given a set of biological sequences, the problem of identifying the motifs is very challenging. This problem has been well studied in computational biology. Identifying motifs through experimental processes is extremely expensive and time consuming. This is one of the factors influencing computational biologists to come up with novel computational methods to predict motifs. Several motif models have been proposed in the literature and for each model numerous algorithms have been devised. Three popular motif models are (l, d)-motif search or Planted Motif Search (PMS), Simple Motif Search (SMS), and Edit-distance based Motif Search (EMS). For PMS and SMS several algorithms have been proposed and implemented. On the other hand, even though some algorithms exist in the literature for the problem of EMS, no implementations of these algorithms are known. This is mainly because the proposed algorithms are complex. In this paper we present an elegant algorithm for EMS. We have implemented this algorithm and compared it against 14 other algorithms in terms of sensitivity and specificity. Our experimental results indicate that the new algorithm is very competitive in practice.
TL;DR: It is shown that binary versions of unary languages in ASPACE(log log n) form a complexity class not contained in NP, and under assumption that NP ≠ co-NP, the standard space translation between unary and binary languages does not work.
Abstract: We shall show that (i) there exists a binary NP-complete language such that its unary coded version is in ASPACE(log log n), (ii) if P ≠ NP, there exists a binary language such that its unary version is in ASPACE(log log n), while the language itself is not in ASPACE(log n). As a consequence, under assumption that P ≠ NP, the standard space translation between unary and binary languages does not work for alternating machines with small space; the equivalence is valid only if s(n) ∈ Ω(n). This is quite different from deterministic and nondeterministic machines, for which the corresponding equivalence holds for each s(n) ∈ Ω(log n), and hence for s(log n) ∈ Ω(log log n). Under assumption that NP ≠ co-NP, we also show that binary versions of unary languages in ASPACE(log log n) form a complexity class not contained in NP.
TL;DR: The necessary theory for hyper-minimization is developed for (bottom-up) deterministic tree automata and the fastest algorithm obtained in this way runs in time, where m is the size of the transition table and n is the number of states of the input tree automaton.
Abstract: Hyper-minimization is a recent automaton compression technique that can reduce the size of an automaton beyond the limits imposed by classical minimization. The additional compression power is enabled by allowing a finite difference in the represented language. The necessary theory for hyper-minimization is developed for (bottom-up) deterministic tree automata. The hyper-minimization problem for deterministic tree automata is reduced to the hyper-minimization problem for deterministic finite-state string automata, for which fast algorithms exist. The fastest algorithm obtained in this way runs in time , where m is the size of the transition table and n is the number of states of the input tree automaton.
TL;DR: This paper shows that the two-dimensional torus TorusTorus(m, n), m, n ≥ 3, is super spanning connected if at least one of m and n is odd and super spanning laceable if bothm and n are even.
Abstract: A k-container of a graph G is a set of k internally disjoint paths between two distinct vertices. A k-container of G is a k*-container if it contains all vertices of G. A graph G is k*-connected if there exists a k*-container between any two distinct vertices, and a bipartite graph G is k*-laceable if there exists a k*-container between any two vertices from different partite sets of G. A k-connected graph (respectively, bipartite graph) G is super spanning connected (respectively, laceable) if G is r*-connected (r*-laceable) for any r with 1 ≤ r ≤ k. This paper shows that the two-dimensional torus Torus(m, n), m, n ≥ 3, is super spanning connected if at least one of m and n is odd and super spanning laceable if both m and n are even. Furthermore, the super spanning connectivity and spanning laceability of tori with faulty elements have been discussed.
TL;DR: The bit-parallel algorithms for the MergedLCS problem are proposed and evaluated in practice showing that they are usually tens times faster than the already published methods.
Abstract: It is often a necessity to compare some sequences to find out how similar they are. There are many similarity measures that can be used, e.g., longest common subsequence, edit distance, sequence alignment. Recently a merged longest common subsequence (MergedLCS) problem was formulated with applications in bioinformatics. We propose the bit-parallel algorithms for the MergedLCS problem and evaluate them in practice showing that they are usually tens times faster than the already published methods.
TL;DR: Besides showing that backward reachability succeeds on many instances of problems covered by general termination results, it is argued that it could predict termination also on interesting instances of the reachability problem that are outside the scope of applicability of such general results.
Abstract: We identify sufficient conditions to automatically establish the termination of a backward reachability procedure for infinite state systems by using well-quasi-orderings. Besides showing that backward reachability succeeds on many instances of problems covered by general termination results, we argue that it could predict termination also on interesting instances of the reachability problem that are outside the scope of applicability of such general results. We work in the declarative framework of Model Checking Modulo Theories that permits us to exploit recent advances in Satisfiability Modulo Theories solving and model-theoretic notions of first-order logic.
TL;DR: In this article, a synchronization game on a deterministic finite automaton with two players, Alice and Bob, whose moves alternate is considered. But the complexity of the synchronization game is not discussed.
Abstract: Two topics are presented: synchronization games and synchronization costs. In a synchronization game on a deterministic finite automaton, there are two players, Alice and Bob, whose moves alternate. Alice wants to synchronize the given automaton, while Bob aims to make her task as hard as possible. We answer a few natural questions related to such games. Speaking about synchronization costs, we consider deterministic automata in which each transition has a certain price. The problem is whether or not a given automaton can be synchronized within a given budget. We determine the complexity of this problem.