Showing papers in "International Journal of Foundations of Computer Science in 2011"
TL;DR: This paper provides basic notions together with the underlying intuition and motivation as well as two examples (a binary counter and transition systems) of "programming" with reaction systems.
Abstract: Reaction systems are a formal framework for investigating processes carried out by biochemical reactions. This paper is an introduction to reaction systems. It provides basic notions together with the underlying intuition and motivation as well as two examples (a binary counter and transition systems) of "programming" with reaction systems. It also provides a tour of some research themes.
102 citations
TL;DR: It is shown that for any finite synchronized prefix code with an n-state decoder, there is a synchronizing word of length O(n2), which applies in particular to Huffman codes.
Abstract: Cerný's conjecture asserts the existence of a synchronizing word of length at most (n - 1)2 for any synchronized n-state deterministic automaton. We prove a quadratic upper bound on the length of a synchronizing word for any synchronized n-state deterministic automaton satisfying the following additional property: there is a letter a such that for any pair of states p, q, one has p·ar = q·as for some integers r, s (for a state p and a word w, we denote by p·w the state reached from p by the path labeled w). As a consequence, we show that for any finite synchronized prefix code with an n-state decoder, there is a synchronizing word of length O(n2). This applies in particular to Huffman codes.
68 citations
TL;DR: It is proved that uniform scattering is indeed possible even for very weak robots, and a provably correct protocol for uniform self-deployment in a grid is presented.
Abstract: We consider the uniform scattering problem for a set of autonomous mobile robots deployed in a grid network: starting from an arbitrary placement in the grid, using purely localized computations, the robots must move so to reach in finite time a state of static equilibrium in which they cover uniformly the grid. The theoretical quest is on determining the minimal capabilities needed by the robots to solve the problem. We prove that uniform scattering is indeed possible even for very weak robots. The proof is constructive. We present a provably correct protocol for uniform self-deployment in a grid. The protocol is fully localized, collision-free, and it makes minimal assumptions; in particular: (1) it does not require any direct or explicit communication between robots; (2) it makes no assumption on robots synchronization or timing, hence the robots can be fully asynchronous in all their actions; (3) it requires only a limited visibility range; (4) it uses at each robot only a constant size memory, hence computationally the robots can be simple Finite-State Machines; (5) it does not need a global localization system but only orientation in the grid (e.g., a compass); (6) it does not require identifiers, hence the robots can be anonymous and totally identical.
54 citations
TL;DR: How the power of defining functions depends on available resources is investigated, and it is demonstrated that with small resources one can define functions exhibiting complex behavior.
Abstract: Reaction systems are a formal model of interactions between biochemical reactions. They consist of sets of reactions, where each reaction is classified by its set of reactants (needed for the reaction to take place), its set of inhibitors (each of which prevents the reaction from taking place), and its set of products (produced when the reaction takes place) – the set of reactants and inhibitors form the resources of the reaction. Each reaction system defines a (transition) function on its set of states. (States here are subsets of an a priori given set of biochemical entities.) In this paper we investigate properties of functions defined by reaction systems. In particular, we investigate how the power of defining functions depends on available resources, and we demonstrate that with small resources one can define functions exhibiting complex behavior.
54 citations
TL;DR: The existence of uniformly recurrent binary words, having bounded Abelian complexity, which admit an infinite number of suffixes which do not begin in an Abelian square is shown.
Abstract: The notion of Abelian complexity of infinite words was recently used by the three last authors to investigate various Abelian properties of words. In particular, using van der Waerden's theorem, they proved that if a word avoids Abelian k-powers for some integer k, then its Abelian complexity is unbounded. This suggests the following question: How frequently do Abelian k-powers occur in a word having bounded Abelian complexity? In particular, does every uniformly recurrent word having bounded Abelian complexity begin in an Abelian k-power? While this is true for various classes of uniformly recurrent words, including for example the class of all Sturmian words, in this paper we show the existence of uniformly recurrent binary words, having bounded Abelian complexity, which admit an infinite number of suffixes which do not begin in an Abelian square. We also show that the shift orbit closure of any infinite binary overlap-free word contains a word which avoids Abelian cubes in the beginning. We also consider the effect of morphisms on Abelian complexity and show that the morphic image of a word having bounded Abelian complexity has bounded Abelian complexity. Finally, we give an open problem on avoidability of Abelian squares in infinite binary words and show that it is equivalent to a well-known open problem of Pirillo–Varricchio and Halbeisen–Hungerbuhler.
54 citations
TL;DR: It is shown that in fact the satisfiability problem for this class of formulas is as hard as the reachability problem for Petri nets.
Abstract: In [19], Yen defines a class of formulas for paths in Petri nets and claims that its satisfiability problem is EXPSPACE-complete. In this paper, we show that in fact the satisfiability problem for this class of formulas is as hard as the reachability problem for Petri nets. Moreover, we salvage almost all of Yen's results by defining a fragment of this class of formulas for which the satisfiability problem is EXPSPACE-complete by adapting his proof.
49 citations
TL;DR: A new relational string verification technique based on multi-track automata is presented that is capable of verifying properties that depend on relations among string variables and enables us to prove that vulnerabilities that result from improper string manipulation do not exist in a given program.
Abstract: Verification of string manipulation operations is a crucial problem in computer security. In this paper, we present a new relational string verification technique based on multi-track automata. Our approach is capable of verifying properties that depend on relations among string variables. This enables us to prove that vulnerabilities that result from improper string manipulation do not exist in a given program. Our main contributions in this paper can be summarized as follows: (1) We formally characterize the string verification problem as the reachability analysis of string systems and show decidability/undecidability results for several string analysis problems. (2) We develop a sound symbolic analysis technique for string verification that over-approximates the reachable states of a given string system using multi-track automata and summarization. (3) We evaluate the presented techniques with respect to several string analysis benchmarks extracted from real web applications.
46 citations
TL;DR: The results of several papers concerning the Cerný conjecture are deduced as consequences of a simple idea that is implicitly used in the literature, but no attempt was made to formalize the proof scheme axiomatically.
Abstract: The results of several papers concerning the Cerný conjecture are deduced as consequences of a simple idea that I call the averaging trick. This idea is implicitly used in the literature, but no attempt was made to formalize the proof scheme axiomatically. Instead, authors axiomatized classes of automata to which it applies.
46 citations
TL;DR: Grain and Trivium are the hardware-oriented finalists of the eSTREAM and their generalized classes of nonlinear feedback shift registers with time varying feedback functions, namely, Grain-like andTrivium-like structures are studied.
Abstract: Grain and Trivium are the hardware-oriented finalists of the eSTREAM. They are both based on nonlinear feedback shift registers. In this paper, we study their generalized classes of nonlinear feedback shift registers with time varying feedback functions, namely, Grain-like and Trivium-like structures. Some interesting results regarding their periods are obtained.
40 citations
TL;DR: This work introduces a new class of weight structures subsuming a range of these models as well as semirings and shows that such weighted automata and Kleene-type regular expressions are expressively equivalent both for finite and infinite words.
Abstract: Quantitative aspects of systems like consumption of resources, output of goods, or reliability can be modeled by weighted automata. Recently, objectives like the average cost or the longtime peak power consumption of a system have been modeled by weighted automata which are not semiring weighted anymore. Instead, operations like limit superior, limit average, or discounting are used to determine the behavior of these automata. Here, we introduce a new class of weight structures subsuming a range of these models as well as semirings. Our main result shows that such weighted automata and Kleene-type regular expressions are expressively equivalent both for finite and infinite words.
39 citations
TL;DR: It is proved that (deterministic) union-freeness of languages does not accelerate regular operations, except for the reversal in the nondeterministic case.
Abstract: We continue the investigation of union-free regular languages that are described by regular expressions without the union operation. We also define deterministic union-free languages as languages accepted by one-cycle-free-path deterministic finite automata, and show that they are properly included in the class of union-free languages. We prove that (deterministic) union-freeness of languages does not accelerate regular operations, except for the reversal in the nondeterministic case.
TL;DR: This paper proves results of the following type for the (n,k)-star graph: if n + (r - 1)k - g(r) vertices are deleted from an (n-k)- star graph, the resulting graph will either be connected or has a large component and small components having at most r - 1 vertices in total.
Abstract: The star graph proposed by [1] has many advantages over the n-cube. However it suffers from having large gaps in the number of possible vertices. The (n,k)-star graph was proposed in [18] to address this issue. Since it is a generalization of the star graph, it retains many of the nice properties of the star graph. There are many different measures of structural integrity of interconnection networks. In this paper, we prove results of the following type for the (n,k)-star graph. If n + (r - 1)k - g(r) vertices are deleted from an (n,k)-star graph, the resulting graph will either be connected or has a large component and small components having at most r - 1 vertices in total. Additional results on conditional vertex connectivity and cycle connectivity will also be given.
TL;DR: Several languages for specifying Markovian population models such as queuing networks and chemical reaction networks differ according to important properties, such as compositionality, expressiveness and succinctness, executability, and ease of use.
Abstract: In this survey, we compare several languages for specifying Markovian population models such as queuing networks and chemical reaction networks. All these languages — matrix descriptions, stochastic Petri nets, stoichiometric equations, stochastic process algebras, and guarded command models — describe continuous-time Markov chains, but they differ according to important properties, such as compositionality, expressiveness and succinctness, executability, and ease of use. Moreover, they provide different support for checking the well-formedness of a model and for analyzing a model.
TL;DR: A comparison between P systems verification using SPIN and NUSMV is realized and the results obtained show that the PROMELA implementation is more adequate, especially for verifying more complex models, such as P systems that model ecosystems.
Abstract: This paper presents an approach to P system verification using the Spin model checker. It proposes a P system implementation in PROMELA, the modeling language accepted by SPIN. It also provides the theoretical background for transforming the temporal logic properties expressed for the P system into properties of the executable implementation. Furthermore, a comparison between P systems verification using SPIN and NUSMV is realized. The results obtained show that the PROMELA implementation is more adequate, especially for verifying more complex models, such as P systems that model ecosystems.
TL;DR: A regression method is presented for deducing a MP system exhibiting the dynamics of an observed metabolic system using the knowledge of the stoichiometry of the system combined with the log-gain principle and integrated with the Least Square Estimation method and with the stepwise regression approximation.
Abstract: MP systems are a class of P systems introduced for modeling metabolic processes. Here a regression method is presented for deducing a MP system exhibiting the dynamics of an observed metabolic system. In the procedure here described the knowledge of the stoichiometry of the system is combined with the log-gain principle of MP systems and is integrated with the Least Square Estimation method and with the stepwise regression approximation.
TL;DR: These computing devices allow non-determinism between the rules ac → a and ac → ā, c ϵ ℕ, thus help to generate languages which cannot be generated using simple SN P systems.
Abstract: An Spiking Neural P system with anti-spikes uses two types of objects called spikes and anti-spikes which can encode binary digits in a natural way. The step when system emits a spike or an anti-spike is associated with symbol 1 and 0, respectively. Here we consider these computing devices as language generators. They allow non-determinism between the rules ac → a and ac → ā, c ϵ ℕ, thus help to generate languages which cannot be generated using simple SN P systems.
TL;DR: By estimating the number of regular expressions that have e as a partial derivative, a lower bound of the average number of mergings of states in and its asymptotic behaviour is computed.
Abstract: The partial derivative automaton () is usually smaller than other nondeterministic finite automata constructed from a regular expression, and it can be seen as a quotient of the Glushkov automaton (). By estimating the number of regular expressions that have e as a partial derivative, we compute a lower bound of the average number of mergings of states in and describe its asymptotic behaviour. This depends on the alphabet size, k, and for growing k's its limit approaches half the number of states in . The lower bound corresponds to consider the automaton for the marked version of the regular expression, i.e. where all its letters are made different. Experimental results suggest that the average number of states of this automaton, and of the automaton for the unmarked regular expression, are very close to each other.
TL;DR: A theoretical chemical/biological solution is presented in terms of membrane computing for the decision version of Ramsey number problem, that is, to decide whether an integer n is the value of Ramsey numbers R(k, l), where k and l are integers.
Abstract: Ramsey numbers deal with conditions when a combinatorial object necessarily contains some smaller given objects It is well known that it is very difficult to obtain the values of Ramsey numbers In this work, a theoretical chemical/biological solution is presented in terms of membrane computing for the decision version of Ramsey number problem, that is, to decide whether an integer n is the value of Ramsey number R(k, l), where k and l are integers
TL;DR: In this article, the authors re-examine the Kuratowski theorem in the setting of formal languages, where by "closure" we mean either Kleene closure or positive closure, and classify languages according to the structure of the algebras they generate under iterations of complement and closure.
Abstract: A famous theorem of Kuratowski states that, in a topological space, at most 14 distinct sets can be produced by repeatedly applying the operations of closure and complement to a given set. We re-examine this theorem in the setting of formal languages, where by "closure" we mean either Kleene closure or positive closure. We classify languages according to the structure of the algebras they generate under iterations of complement and closure. There are precisely 9 such algebras in the case of positive closure, and 12 in the case of Kleene closure. We study how the properties of being open and closed are preserved under concatenation. We investigate analogues, in formal languages, of the separation axioms in topological spaces; one of our main results is that there is a clopen partition separating two words if and only if the words do not commute. We can decide in quadratic time if the language specified by a DFA is closed, but if the language is specified by an NFA, the problem is PSPACE-complete.
TL;DR: This paper considers a new characteristic, residual closeness, which is more sensitive than the well-known vulnerability measures and measures the network resistance evaluating closeness after removal of vertices or links.
Abstract: The vulnerability of a network measures the resistance of the network to disruption of operation after the failure of certain stations or communication links. If we think of a graph as modeling a network, several vulnerability measures have been used to describe the stability of networks, including connectivity, toughness, scattering number, binding number and integrity. We consider a new characteristic, residual closeness which is more sensitive than the well-known vulnerability measures. Residual closeness measures the network resistance evaluating closeness after removal of vertices or links. In this paper, closeness, vertex residual closeness (VRC) and normalized vertex residual closeness (NVRC) of wheels and some related networks namely gear and friendship graph are calculated, and exact values are obtained.
TL;DR: This work focuses on the descriptional complexity of the conversion of regular expressions to equivalent finite automata and vice versa, to the computational complexity of problems on regular-like expressions such as membership, inequivalence, and non-emptiness of complement.
Abstract: We summarize results on the complexity of regular(-like) expressions and tour a fragment of the literature. In particular we focus on the descriptional complexity of the conversion of regular expressions to equivalent finite automata and vice versa, to the computational complexity of problems on regular-like expressions such as, e.g., membership, inequivalence, and non-emptiness of complement, and finally on the operation problem measuring the required size for transforming expressions with additional language operations (built-in or not) into equivalent ordinary regular expressions.
TL;DR: The definition for closeness is generalized and its properties are explored and some formulas for easy calculation of residual closeness are given.
Abstract: In the last few years a new definition for closeness has been established because of the ability to measure not connected graphs and the possibility to create convenient formulas for calculations Based on this definition a new, more sensitive measure for network vulnerability is created - residual closeness The residual closeness utilizes closeness received after the removal of a link or a vertex and its links In this article some formulas for easy calculation of residual closeness are given The definition for closeness is generalized and its properties are explored
TL;DR: It is proved that recognizer P systems with active membranes using polynomial space characterize the complexity class PSPACE.
Abstract: We prove that recognizer P systems with active membranes using polynomial space characterize the complexity class PSPACE. This result holds for both confluent and nonconfluent systems, and independently of the use of membrane division rules.
TL;DR: It is shown that the state complexity of the former combined operation is considerably less than the mathematical composition of the state complexities of catenation and union, while the state complex of the latter one is equal to the mathematical compositions of thestate complexities ofCatenation, union, and intersection.
Abstract: In this paper, we study the state complexities of two particular combinations of operations: catenation combined with union and catenation combined with intersection. We show that the state complexity of the former combined operation is considerably less than the mathematical composition of the state complexities of catenation and union, while the state complexity of the latter one is equal to the mathematical composition of the state complexities of catenation and intersection.
TL;DR: This work provides efficient techniques, that are called contraction and extension, to reduce multivariate (and univariate) multiplication to balanced bivariate multiplication and demonstrates good speedup on multi-cores in Cilk++.
Abstract: In symbolic computation, polynomial multiplication is a fundamental operation akin to matrix multiplication in numerical computation. We present efficient implementation strategies for FFT-based dense polynomial multiplication targeting multi-cores. We show that balanced input data can maximize parallel speedup and minimize cache complexity for bivariate multiplication. However, unbalanced input data, which are common in symbolic computation, are challenging. We provide efficient techniques, that we call contraction and extension, to reduce multivariate (and univariate) multiplication to balanced bivariate multiplication. Our implementation in Cilk++ demonstrates good speedup on multi-cores.
TL;DR: In this paper, it was shown that a linear ordering is algebraic if and only if it can be represented as the lexicographic ordering of a deterministic context-free language.
Abstract: An algebraic linear ordering is a component of the initial solution of a first-order recursion scheme over the continuous categorical algebra of countable linear orderings equipped with the sum operation and the constant 1. Due to a general Mezei-Wright type result, algebraic linear orderings are exactly those isomorphic to the linear ordering of the leaves of an algebraic tree. Using Courcelle's characterization of algebraic trees, we obtain the fact that a linear ordering is algebraic if and only if it can be represented as the lexicographic ordering of a deterministic context-free language. When the algebraic linear ordering is a well-ordering, its order type is an algebraic ordinal. We prove that the Hausdorff rank of any scattered algebraic linear ordering is less than ωω. It follows that the algebraic ordinals are exactly those less than ωωω.
TL;DR: An n-state nondeterministic finite automaton with a three-letter input alphabet that requires exactly α deterministic states is defined.
Abstract: A number α, in the range from n to 2n, is magic for n with respect to a given alphabet size s, if there is no minimal nondeterministic finite automaton of n states and s input symbols whose equivalent minimal deterministic finite automaton has α states. We show that in the case of a ternary alphabet, there are no magic numbers. For all n and α satisfying n ⩽ α ⩽ 2n, we define an n-state nondeterministic finite automaton with a three-letter input alphabet that requires exactly α deterministic states.
TL;DR: This parameter iv(G) of G relative to v is the minimum cardinality of a maximal independent set in G that contains v, and an algorithm for the average lower independence number of any graph is offered.
Abstract: For a vertex v of a graph G = (V,E), the independent domination number (also called the lower independence number) iv(G) of G relative to v is the minimum cardinality of a maximal independent set in G that contains v. The average lower independence number of G is $i_{av} \,(G)\, = \,\frac{1} {{|V\,(G)|}}\,\sum {_{v\, \in \,V\,(G)} \,i_v \,(G)} $. In this paper, this parameter is defined and examined, also the average lower independence number of gear graphs is considered. Then, an algorithm for the average lower independence number of any graph is offered.
TL;DR: This paper proposes efficient algorithms for disjoint-paths and fault-tolerant routings on the recursive dual-net, a newly proposed interconnection network for of massive parallel computers.
Abstract: The recursive dual-net is a newly proposed interconnection network for massive parallel computers. The recursive dual-net is based on recursive dual-construction of a symmetric base network. A k-level dual-construction for k > 0 creates a network containing (2n0)2k/2 nodes with node-degree d0 + k, where n0 and d0 are the number of nodes and the node-degree of the base network, respectively. The recursive dual-net is node and edge symmetric and can contain huge number of nodes with small node-degree and short diameter. Disjoint-paths routing and fault-tolerant routing are fundamental and critical issues for the performance of an interconnection network. In this paper, we propose efficient algorithms for disjoint-paths and fault-tolerant routings on the recursive dual-net.
TL;DR: Extended definitions and characterizations of the classical notions of APN and maximum nonlinear Boolean functions are presented to deal with the case of mappings from a finite group K to another one N with the possibility that one or both groups are non-Abelian.
Abstract: The purpose of this paper is to present extended definitions and characterizations of the classical notions of APN and maximum nonlinear Boolean functions to deal with the case of mappings from a finite group K to another one N with the possibility that one or both groups are non-Abelian.