49,167 research outputs found

    How to Go Beyond Turing with P Automata: Time Travels, Regular Observer !-Languages, and Partial Adult Halting

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    In this paper we investigate several variants of P automata having in nite runs on nite inputs. By imposing speci c conditions on the in nite evolution of the systems, it is easy to nd ways for going beyond Turing if we are watching the behavior of the systems on in nite runs. As speci c variants we introduce a new halting variant for P automata which we call partial adult halting with the meaning that a speci c prede ned part of the P automaton does not change any more from some moment on during the in nite run. In a more general way, we can assign !-languages as observer languages to the in nite runs of a P automaton. Speci c variants of regular !-languages then, for example, characterize the red-green P automata

    On Languages of P Automata

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    P automata are accepting computing devices combining features of classical automata and membrane systems. In this paper we introduce P n-stack-automata, a restricted class of P automata that mimics the behaviour of n-stack automata. We show that for n = 1 these constructs describe the context-free language class and for n = 3 the class of quasi-realtime languages

    On the Complexity of Limit Sets of Cellular Automata Associated with Probability Measures

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    We study the notion of limit sets of cellular automata associated with probability measures (mu-limit sets). This notion was introduced by P. Kurka and A. Maass. It is a refinement of the classical notion of omega-limit sets dealing with the typical long term behavior of cellular automata. It focuses on the words whose probability of appearance does not tend to 0 as time tends to infinity (the persistent words). In this paper, we give a characterisation of the persistent language for non sensible cellular automata associated with Bernouilli measures. We also study the computational complexity of these languages. We show that the persistent language can be non-recursive. But our main result is that the set of quasi-nilpotent cellular automata (those with a single configuration in their mu-limit set) is neither recursively enumerable nor co-recursively enumerable

    Unary Pushdown Automata and Straight-Line Programs

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    We consider decision problems for deterministic pushdown automata over a unary alphabet (udpda, for short). Udpda are a simple computation model that accept exactly the unary regular languages, but can be exponentially more succinct than finite-state automata. We complete the complexity landscape for udpda by showing that emptiness (and thus universality) is P-hard, equivalence and compressed membership problems are P-complete, and inclusion is coNP-complete. Our upper bounds are based on a translation theorem between udpda and straight-line programs over the binary alphabet (SLPs). We show that the characteristic sequence of any udpda can be represented as a pair of SLPs---one for the prefix, one for the lasso---that have size linear in the size of the udpda and can be computed in polynomial time. Hence, decision problems on udpda are reduced to decision problems on SLPs. Conversely, any SLP can be converted in logarithmic space into a udpda, and this forms the basis for our lower bound proofs. We show coNP-hardness of the ordered matching problem for SLPs, from which we derive coNP-hardness for inclusion. In addition, we complete the complexity landscape for unary nondeterministic pushdown automata by showing that the universality problem is Π2P\Pi_2 \mathrm P-hard, using a new class of integer expressions. Our techniques have applications beyond udpda. We show that our results imply Π2P\Pi_2 \mathrm P-completeness for a natural fragment of Presburger arithmetic and coNP lower bounds for compressed matching problems with one-character wildcards

    A Class of P Automata for Characterizing Context-free Languages

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    We present a characterization of context-free languages in terms of a restricted class of P automata (P systems accepting strings of symbols using symport/antiport communication rules). The characterization is based on the form of the rules used by the system

    On the Classes of Languages Characterized by Generalized P Colony Automata

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    We study the computational power of generalized P colony automata and show how it is in uenced by the capacity of the system (the number of objects inside the cells of the colony) and the types of programs which are allowed to be used (restricted and unrestricted com-tape and all-tape programs, or programs allowing any kinds of rules)

    A Prolog toolkit for formal languages and automata

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    This paper describes the first version of P-flat, a collection of Prolog predicates that aims to provide a pedagogical implementation of concepts and algorithms taught in Formal Languages and Automata Theory (FLAT) courses. By ?pedagogical implementation? we mean on the one hand that students should be able to easily map the implementation to the mathematical definitions given in lectures, and on the other hand that the toolkit should provide a library for students to implement further concepts and algorithms. In both cases the goal is to make students more confident in defining and manipulating the various kinds of languages and automata at a level beyond the one provided by visual simulators of automata. As such, P-flat is not intended to replace but rather complement existing graphical tools. We believe the declarative, non-deterministic, and interactive nature of Prolog helps in building an executable specification of FLAT concepts and definitions that can be actively extended and explored by students, in order to achieve the stated goal

    On Deciding Linear Arithmetic Constraints Over p-adic Integers for All Primes

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    Given an existential formula Φ of linear arithmetic over p-adic integers together with valuation constraints, we study the p-universality problem which consists of deciding whether Φ is satisfiable for all primes p, and the analogous problem for the closely related existential theory of Büchi arithmetic. Our main result is a coNEXP upper bound for both problems, together with a matching lower bound for existential Büchi arithmetic. On a technical level, our results are obtained from analysing properties of a certain class of p-automata, finite-state automata whose languages encode sets of tuples of natural numbers
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