A note on emptiness for alternating finite automata with a one-letter alphabet

We present a new proof of PSPACE-hardness of the emptiness problem for alternating finite automata with a singleton alphabet. This result was shown by Holzer (1995) who used a proof relying on a series of reductions from several papers. The new proof is simple, direct and self-contained.     

Three-way automata on rectangular tapes over a one-letter alphabet

Necessary conditions for the languages recognized by three-way automata on tapes over a one-letter alphabet are obtained. These conditions have a simple algebraic form. Using these conditions, nondeterministic three-way automata are proved to be more powerful than deterministic automata and various decision problems for the three-way automata are solved.     

The concept of duality for automata over a changing alphabet and generation of a free group by such automata

In the paper, we deal with the notion of an automaton over a changing alphabet, which generalizes the concept of a Mealy-type automaton. We modify the methods based on the idea of a dual automaton and its action used by B. Steinberg et al. (2011) and M. Vorobets and Ya. Vorobets (2007, 2010) [16], [17] and [18] and adapt them to automata over a changing alphabet. We show that this modification provides some naturally defined automaton representations of a free nonabelian group by a 2-state automaton over a changing alphabet.     

Tree automata with one memory set constraints and cryptographic protocols

We introduce a class of tree automata that perform tests on a memory that is updated using function symbol application and projection. The language emptiness problem for this class of tree automata is shown to be in DEXPTIME.We also introduce a class of set constraints with equality tests and prove its decidability by completion techniques and a reduction to tree automata with one memory.Finally, we show how to apply these results to cryptographic protocols. We introduce a class of cryptographic protocols and show the decidability of secrecy for an arbitrary number of agents and an arbitrary number of (concurrent or successive) sessions, provided that only a bounded number of new data is generated. The hypothesis on the protocol (a restricted copying ability) is shown to be necessary: without this hypothesis, we prove that secrecy is undecidable, even for protocols without nonces.     

PPM with the extended alphabet

In the following paper we propose modification of Prediction by Partial Matching (PPM)—a lossless data compression algorithm, which extends an alphabet, used in the PPM method, to long repeated strings. Usually the PPM algorithm’s alphabet consists of 256 characters only. We show, on the basis of the Calgary corpus [T.C. Bell, J. Cleary, I.H. Witten, Text compression. Advanced Reference Series, Prentice Hall, Englewood Cliffs, New Jersey, 1990], that for ordinary files such a modification improves the compression performance in lower, but not greater than 10, orders. However, for some kind of files, this modification gives much better compression performance than any known lossless data compression algorithm.     

General method of testing the compatibility of interacting automata with finite memory

A method is proposed for compatibility analysis of two interacting partial nondeterministic automata A and B specified in a first-order language with monadic predicates. In contrast to a method proposed earlier, no restrictions are imposed on the form of specification of the automaton B. These investigations were partially supported by INTAS grant 96-0760. Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 25–37, November–December, 1999.     

Error correcting capability of cellular automata based associative memory

This paper reports the error correcting capability of an associative memory model built around the sparse network of cellular automata (CA). Analytical formulation supported by experimental results has demonstrated the capability of CA based sparse network to memorize unbiased patterns while accommodating noise. The desired CA are evolved with an efficient formulation of simulated annealing (SA) program. The simple, regular, modular, and cascadable structure of CA based associative memory suits ideally for design of low cost high speed online pattern recognizing machine with the currently available VLSI technology.     

拟(h,k)存贮有限自动机的可逆性

主要研究拟(h,k)阶存贮有限自动机的延迟k步与k+1步弱可逆性,以及它的弱逆,得到了拟(h,k)阶存贮有限自动机的延迟k步与k+1步弱可逆的充分必要条件,并且通过所得结果可以比较简便地构造出延迟k步与k+1步弱可逆拟(h,k)阶存贮有限自动机的延迟k步与k+1步弱逆.     

Languages accepted by systolic Y-tree automata: structural characterizations

In this paper closure properties and decision problems for families of languages accepted by deterministic and nondeterministic systolic binary Y-tree automata are studied. Non closure results under basic language operations are stated by means of new nonacceptability criteria for these classes of automata. Necessary and sufficient conditions are given in terms of the shape of the underlying Y-tree, for the closure under -free regular substitution, concatenation, inverse homomorfism and for the closure under right concatenation with and quotient by finite sets. Moreover in the nondeterministic case necessary and sufficient conditions are given again in terms of the shape of the underlying Y-tree for the closure under right concatenation with regular sets and for the decidability of the problems of emptiness, finiteness, equivalence and co-emptiness. A sufficient condition is given for the decidability of the stability problem, in the deterministic case, while some undecidability results are proved in the nondeterministic case.Work partially supported by the Italian Ministry of the University and of Scientific Research in the framework of the project Modelli e specifiche per sistemi concorrenti.     

Two memory bounds for the recognition of primes by automata

This paper establishes two bounds for the rate of growth of memory in automata which recognize the set of primes.This research has been supported in part by National Science Foundation Grant GP-6426.     

Recording the use of memory in right-boundary grammars and push-down automata

Summary Within the framework of coordinated pair systems a push-down automatonA is formalized as an ordered pair (G ₁,G ₂) of grammars, whereG ₁ is a right-linear grammar modelling the finite state control ofA and the reading of the input ofA, and G₂ is a right-boundary grammar modelling the push-down store ofA. In this paper we present a systematic investigation into the use of memory of right-boundary grammars. Various methods of recording the use of memory are introduced. The results presented concern regularity properties of each of the methods and the interrelationships of the records obtained by different methods. Finally the translation of these results to the level of push-down automata (coordinated pair systems) is discussed.