International Journal of Foundations of Computer Science

We give a canonical representation for minimal acyclic deterministic finite automata (MADFA) with n states over an alphabet of k symbols. Using this normal form, we present a method for the exact generation of MADFAs. This method avoids a rejection phase that would be needed if a generation algorithm for a larger class of objects that contains the MADFAs were used. We give upper and lower bounds for MADFAs enumeration and some exact formulas for small values of n.

We consider cooperating distributed grammar systems with the components working in different derivation modes as well as with regular sets as additional start conditions for the components. With the classical derivation modes ≤ k and = k as well as with the internally hybrid mode (≥ ℓ∧ ≤ k) we obtain a characterization of the family of recursively enumerable languages even with only one component, with the derivation modes *, t, and ≥ k as well as with the internally hybrid mode (t∧ ≥ k) two components working in the same mode and only one common regular set for both components yield computational completeness. For the internally hybrid modes (t∧ ≤ k) and (t∧ = k) we only obtain languages of finite index, but combining one component working in one of these modes (t∧ ≤ k) and (t∧ = k) with a component working in one of the modes * and ≥ k we again obtain a characterization of the family of recursively enumerable languages.

We explore the connection between the concepts of complexity, information and energy. Several open questions are formulated.

The simulation of weak restarting automata, i.e., classical restarting automata accepting exactly the regular languages, by finite automata is studied. Some of the trade-offs in the number of states when changing the representation are known. Here we continue the investigation in order to draw an almost complete picture of the descriptional power gained in the additional structural resources of weak restarting automata. In particular, for det-RR(1)-simulations of nondeterministic finite automata we obtain the same tight bounds as for simulations of R(1)-automata, though in some cases the latter class is much more efficient than the former. Moreover, the DFA-simulation of det-RR(1)-automata is considered. The shown bounds are of factorial order and are tight. The constructions are via alternating finite automata to DFAs. So, in addition, an upper bound for the AFA-simulation is obtained.

In this paper, the descriptional complexity of extended finite splicing systems is studied. These systems are known to generate exactly the class of regular languages. Upper and lower bounds are shown relating the size of these splicing systems, defined as the total length of the rules and the initial language of the system, to the size of their equivalent minimal nondeterministic finite automata (NFA). In addition, an accepting model of extended finite splicing systems is studied. Using this variant one can obtain systems which are more than polynomially more succinct than the equivalent NFA or generating extended finite splicing system.

We study lower bounds on space and input head reversals for deterministic, nondeterministic, and alternating Turing machines accepting nonregular languages. Three notions of space, namely strong, middle, weak are considered, and another notion, called accept, is introduced. In all cases, we obtain tight lower bounds. Moreover, we show that, while for determinism and nondeterminism such lower bounds are optimal even with respect to unary languages, for alternation optimal lower bounds for unary languages turn out to be strictly higher than those for languages over alphabets with two or more symbols.

We define a complexity measure on context-free grammars called end. Roughly speaking, for a context-free grammar G, end_G(n) measures the distance of variables from the ends of sentential forms along the derivations of words in L(G) of length n. We prove in a constructive way the regularity of L(G)wheneverend_G(n)is constant. Yet, we improve on this by showing that ifL(G)is nonregular thenend_G(n) = Ω_∞(logn). We establish the optimality of such bound. Finally, we show that, in case of unambiguous context-free grammars, the end lower bound for generating nonregular languages turns out to be linear.

Insertion-deletion operations are much investigated in linguistics and in DNA computing and several characterizations of Turing computability and characterizations or representations of languages in Chomsky hierarchy were obtained in this framework.

In this note we contribute to this research direction with a new characterization of this type, as well as with representations of regular and context-free languages, mainly starting from context-free insertion systems of as small as possible complexity. For instance, each recursively enumerable language L can be represented in a way similar to the celebrated Chomsky-Schützenberger representation of context-free languages, i.e., in the form L = h(L(γ) ∩ D), where γ is an insertion system of weight (3, 0) (at most three symbols are inserted in a context of length zero), h is a projection, and D is a Dyck language. A similar representation can be obtained for regular languages, involving insertion systems of weight (2,0) and star languages, as well as for context-free languages – this time using insertion systems of weight (3, 0) and star languages.

Parallel communicating grammar systems are language generating devices consisting of several grammars which derive synchronously their sentential forms and communicate with each other by sending their sentential forms to another component on request. Due to collaboration, grammar systems with context-free components are more powerful than a single context-free grammar; they even can generate all recursively enumerable languages.

In natural languages, there occur constructions that cannot be modelled by context-free languages. Three important phenomena are the so-called multiple agreements, crossed agreements and replication which are represented by the three non-context-free languages K₁ = { aⁿbⁿcⁿ | n ≥ 1 }, K₂ = { aⁿb^mcⁿd^m | m ≥ 1, n ≥ 1 }, and K₃ = { ww | w ∈ { a, b }⁺}, respectively.

In the present paper, we give parallel communicating grammar systems (PC grammar systems) that are context-free and that generate the language K₂, working in different modes. In two cases, the results are optimal.

The Wireless Parallel Turing Machine (WPTM) is a new computational model recently introduced and studied by the authors. Its design captures important features of wireless mobile computing. In this paper we survey some results related to the descriptive complexity aspects of the new model. In particular, we show a tight relationship about (a) wireless parallel computing, (b) alternating, and (c) synchronized alternating Turing machines. This relationship opens, e.g., the road to circuit complexity by offering an elegant WPTM characterization of bounded-fan-in uniform circuit families, such as NC and NCⁱ. The structural properties of computational graphs of WPTM computations inspire definitions of new complexity measures capturing important aspects of wireless computations: energy consumption and the number of broadcasting channels used during computation. These measures do not seem to have direct counterparts in alternating computations. We mention results related to these new structural measures, e.g., a polynomial time–bounded complexity hierarchy based on channel complexity, lying between P and PSPACE which seems to be incomparable to the standard polynomial–time alternating hierarchy.

We give a brief survey of results that use “reversal-bounded counters” in studying reachability problems for various classes of transition systems. We also discuss the connection between the decidability of reachability in counter machines and the solvability of certain Diophantine equations.

In this paper we analyze the dynamics of one-dimensional piecewise maps. We show that one-dimensional piecewise affine maps are equivalent to pseudo-billiard or so called “strange billiard” systems. We also show that use of more general classes of functions lead to undecidability of reachability problem for one-dimensional piecewise maps.

We present an approach to verification of parameterized systems, which is based on program transformation technique known as supercompilation. In this approach the statements about safety properties of a system to be verified are translated into the statements about properties of the program that simulates and tests the system. Supercompilation is used then to establish the required properties of the program. In this paper we show that reachability analysis performed by supercompilation can be seen as the proof of a correctness condition by induction. We formulate suitable induction principles and proof strategies and illustrate their use by examples of verification of parameterized protocols.

In this paper, we consider the finite tiling problem which was proved undecidable in the Euclidean plane by Jarkko Kari, see [5]. Here, we prove that the same problem for the hyperbolic plane is also undecidable.

Recently, it has been shown that for any higher order pushdown system and for any regular set of configurations, the set , is regular. In this paper, we give an alternative proof of this result for second order automata. Our construction of automaton for recognizing is explicit. The termination of saturation procedure used is obvious. It gives EXPTIME bound on size of the automaton recognizing if there is no alternation present in and in the automaton recognizing .

The conventional forbidden state problem for discrete event systems is concerned with the issue of synthesizing a maximally permissive control policy to prevent a discrete event system from reaching any forbidden state during the course of its computation. In this paper, we regard the forbidden state problem as a decision problem, and investigate the decidability/complexity issue of the problem under two new types of control policies, namely, non-blocking and fair policies, for finite state systems and Petri nets.

Checkpoint is a designated place in a program at which normal process is interrupted specifically to preserve the status information necessary to allow resumption of processing at a later time. A checkpoint algorithm for mobile distributed systems needs to handle many new issues like: mobility, low bandwidth of wireless channels, lack of stable storage on mobile nodes, disconnections, limited battery power and high failure rate of mobile nodes. These issues make traditional checkpointing techniques unsuitable for such environments. Minimum-process coordinated checkpointing is an attractive approach to introduce fault tolerance in mobile distributed systems transparently. This approach is domino-free, requires at most two checkpoints of a process on stable storage, and forces only a minimum number of processes to checkpoint. But, it requires extra synchronization messages, blocking of the underlying computation or taking some useless checkpoints. In this paper, we design a minimum-process checkpointing algorithm for mobile distributed systems, where no useless checkpoint is taken. We reduce the blocking of processes by allowing the processes to do their normal computations, send messages and receive selective messages during their blocking period.

In this paper we study subword inequalities, that is, inequalities between the number of occurrences of certain scattered subwords in a word. The problem of deciding whether a subword inequality holds for all words was proposed in [5]. We provide partial results describing a few cases in which the subword inequalities hold. Whether a subword inequality falls in these categories is decidable. However, the general question remains open.

In this paper, we propose a solution for the problem of capturing an intruder in two popular interconnection topologies namely, the mesh and the torus. A set of agents collaborate to capture a hostile intruder in the network. While the agents can move in the network one hop at a time, the intruder is assumed to be arbitrarily fast i.e. it can traverse any number of nodes contiguously as far as there are no agents in those nodes. Here we consider a new version of the problem where each agent can replicate new agents when needed, i.e. the algorithm starts with a single agent and new agents are created on demand. We define a new class of algorithms for capturing an intruder. In particular, we propose two different algorithms on mesh and torus networks and we will later discuss about the merits of each algorithm based on some performance criteria.

We say a family of strings over an alphabet is an UMFF if every string has a unique maximal factorization over . Foundational work by Chen, Fox and Lyndon established properties of the Lyndon circ-UMFF, which is based on lexicographic ordering. Commencing with the circ-UMFF related to V-order, we then proved analogous factorization families for a further 32 Block-like binary orders. Here we distinguish between UMFFs and circ-UMFFs, and then study the structural properties of circ-UMFFs. These properties give rise to the complete construction of any circ-UMFF. We prove that any circ-UMFF is a totally ordered set and a factorization over it must be monotonic. We define atom words and initiate a study of u, v-atoms. Applications of circ-UMFFs arise in string algorithmics.