Reversible pushdown automata

Reversible pushdown automata are deterministic pushdown automata that are also backward deterministic. Therefore, they have the property that any configuration occurring in any computation has exactly one predecessor. In this paper, the computational capacity of reversible computations in pushdown automata is investigated and turns out to lie properly in between the regular and deterministic context-free languages. Furthermore, it is shown that a deterministic context-free language cannot be accepted reversibly if more than realtime is necessary for acceptance. Closure properties as well as decidability questions for reversible pushdown automata are studied. Finally, we show that the problem to decide whether a given nondeterministic or deterministic pushdown automaton is reversible is P-complete, whereas it is undecidable whether the language accepted by a given nondeterministic pushdown automaton is reversible.     

Quasi-rocking real-time pushdown automata

A pushdown automaton (PDA) is quasi-rocking if it preserves the stack height for no more than a bounded number of consecutive moves. Every PDA can be transformed into an equivalent one that is quasi-rocking and real-time and every finite-turn (one-turn) PDA can be transformed into an equivalent one that is quasi-rocking or real-time. The quasi-rocking [quasi-rocking in the increasing mode, and quasi-rocking in the decreasing mode] real-time restriction in finite-turn (one-turn) PDAs coincides with the double Greibach [reverse Greibach, and Greibach] form in nonterminal-bounded (linear) context-free grammars. This provides complete grammatical characterizations of quasi-rocking and/or real-time (finite-turn and one-turn) PDAs and, together with known relations and other relations proved in the present paper, yields an extended hierarchy of PDA languages. Basic decision properties for PDAs can be stated in stronger forms by using the quasi-rocking and real-time restrictions and their undecidability/decidability status rests on the way PDAs quasi-rock.     

Analyzing probabilistic pushdown automata

The paper gives a summary of the existing results about algorithmic analysis of probabilistic pushdown automata and their subclasses.     

On jump-deterministic pushdown automata

The realtime one-state deterministic pushdown automata with jumps define the family of deterministic languages. A simplified regularity test for deterministic languages can be derived from this fact.     

Teams of pushdown automata

We introduce team pushdown automata (PDAs) as a theoretical framework capable of modelling various communication and cooperation strategies in complex, distributed systems. Team PDAs are obtained by augmenting distributed PDAs with the notion of team cooperation or, alternatively, by augmenting team automata with pushdown memory. In a team PDA, several PDAs work as a team on the input word placed on a common one-way input tape. At any moment in time one team of PDAs, each with the same symbol on top of its stack, is active: each PDA in the active team replaces the topmost symbol of its stack and changes state, while the current input symbol is read from the input tape by a common reading head. The teams are formed according to the team cooperation strategy of the team PDA and may vary from one moment to the other. Based on the notion of competence, we introduce a variety of team cooperation strategies. If all stacks are empty when the input word has been completely read, then this word is part of the language accepted by the team PDA. Here we focus on the accepting capacity of team PDA.     

Measuring nondeterminism in pushdown automata

The amount of nondeterminism that a pushdown automaton requires to recognize an input string can be measured by the minimum number of guesses that it must make to accept the string, where guesses are measured in bits of information. When this quantity is unbounded, the rate at which it grows as the length of the string increases serves as a measure of the pushdown automaton's “rate of consumption” of nondeterminism. We show that this measure is similar to other complexity measures in that it gives rise to an infinite hierarchy of complexity classes of context-free languages differing in the amount of the resource (in this case, nondeterminism) that they require. In addition, we show that there are context-free languages that can only be recognized by a pushdown automaton whose nondeterminism grows linearly, resolving an open problem in the literature. In particular, the set of palindromes is such a language.     

Semitopological semirings and pushdown automata

This paper deals with algebraic power series over a commutative semiringA. A characteristization result states that a power series is algebraic if and only if it is the behavior of a proper pushdown automaton.To achieve this result some topological concepts are needed to be able to solve linear equations over semirings.     

Conjunctive grammars and alternating pushdown automata

In this paper we introduce a variant of alternating pushdown automata, synchronized alternating pushdown automata, which accept the same class of languages as those generated by conjunctive grammars.     

Equivalence of deterministic pushdown automata revisited

This paper briefly analyzes main ideas underlying the comparison algorithm that made it possible to prove the equivalence of deterministic pushdown automata. An example of using this algorithm is presented. The relationship of this algorithm with other results in this area is shown. Moreover, the decidability of problems associated with some classes of formal grammars is established. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 24–39, March–April 2007.     

格值下推自动机与格值上下文无关文法

引入了格值下推自动机、格值上下文无关文法及它们的语言的概念,证明了格值下推自动机以两种不同方式接受的语言类的等价性,研究了格值Chomsky范式文法、格值上下文无关文法及其派生所产生的语言的等价条件,揭示了在一定条件下,格值下推自动机接受的语言类与格值上下文无关文法产生的语言类的等价性,证明了有理格值语言均被格值下推自动机识别。     

Language recognition by two-way deterministic pushdown automata

It is proved that any bounded context-free language can be recognized by a two-way deterministic automaton with a finite-rotary counter.Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 177–181, November–December 2004.This revised version was published online in April 2005 with a corrected cover date.     

A note on non-singular deterministic pushdown automata

The non-singular deterministic pushdown automata were first defined by Valiant as an example of a class of machines with a decidable equivalence problem [3]. No algorithm currently exist for deciding whether or not a deterministic pushdown automation is non-singular, so the applicability of Valiant's equivalence decision procedure cannot be readily (if ever) determined. In this paper, it is shown that the equivalence problem for non-singular automata is reducible to the problem of deciding whether or not a deterministic pushdown automaton is non-singular.     

On regular tree languages and deterministic pushdown automata

The theory of formal string languages and of formal tree languages are both important parts of the theory of formal languages. Regular tree languages are recognized by finite tree automata. Trees in their postfix notation can be seen as strings. This paper presents a simple transformation from any given (bottom-up) finite tree automaton recognizing a regular tree language to a deterministic pushdown automaton accepting the same tree language in postfix notation. The resulting deterministic pushdown automaton can be implemented easily by an existing parser generator because it is constructed for an LR(0) grammar, and its size directly corresponds to the size of the deterministic finite tree automaton. The class of regular tree languages in postfix notation is a proper subclass of deterministic context-free string languages. Moreover, the class of tree languages which are in their postfix notation deterministic context-free string languages is a proper superclass of the class of regular tree languages.