Pushdown automaton

About: Pushdown automaton is a research topic. Over the lifetime, 1868 publications have been published within this topic receiving 35399 citations.

Degrees of Nondeterminism for Pushdown Automata

Abstract: Savitch and Vermeir in [7] introduced two measures for nondeterminism of pushdown automata and showed interestingly that the second measure yields an infinite hierarchy of language families between the deterministic context-free and general context-free languages. However, the proof given in [7] for this hierarchy theorem was incorrect. In this paper, we show that all the languages used in [7] to separate different families of the hierarchy actually belong to the first level above the DCFLs. We give a new proof for the hierarchy theorem. We also introduce a new and intuitive measure for nondeterminism and show that it is equivalent to Savitch and Vermeir's second measure.

On Multi-stack Visibly Pushdown Languages

Abstract: We contribute to the theory of formal languages of visibly multistack pushdown automata (MVPA). First, we show closure under the main operations and decidability of the main decision problems for the class of MVPA restricted to computations where a symbol can be popped out of a stack S only if it was pushed within the last k contexts of S, for a given k (in a context only one stack can be pushed or popped). In particular, this class turns out to be determinizable. Second, we show the closure under complement of the class of languages accepted by ordered MVPA (where the limitation is that a stack can be popped only if all the lower indexed stacks are empty). This gains decidability of universality, inclusion and equivalence for this class. As a further contribution, we compare the classes of languages accepted by different models of MVPA.

Subtree matching by deterministic pushdown automata

Abstract: Subtree matching is an important problem in Computer Science on which a number of tasks, such as mechanical theorem proving, term-rewriting, symbolic computation and non-procedural programming languages are based on. A systematic approach to the construction of subtree pattern matchers by deterministic pushdown automata, which read subject trees in prefix notation, is presented. The method is analogous to the construction of string pattern matchers: for a given pattern, a nondeterministic pushdown automaton is created and then it is determinised. In addition, it is shown that the size of the resulting deterministic pushdown automata directly corresponds to the size of the existing string pattern matchers based on finite automata.

Inclusion Problems for One-Counter Systems

Abstract: We study the decidability and complexity of verification problems for infinite-state systems. A fundamental question in formal verification is if the behaviour of one process is reproducible by another. This inclusion problem can be studied for various models of computation and behavioural preorders. It is generally intractable or even undecidable already for very limited computational models. The aim of this work is to clarify the status of the decidability and complexity of some well-known inclusion problems for suitably restricted computational models. In particular, we address the problems of checking strong and weak simulation and trace inclusion for processes definable by one-counter automata (OCA), that consist of a finite control and a single counter ranging over the non-negative integers. We take special interest of the subclass of one-counter nets (OCNs), that cannot fully test the counter for zero and which is subsumed both by pushdown automata and Petri nets / vector addition systems. Our new results include the PSPACE-completeness of strong and weak simulation, and the undecidability of trace inclusion for OCNs. Moreover, we consider semantic preorders between OCA/OCN and finite systems and close some gaps regarding their complexity. Finally, we study deterministic processes, for which simulation and trace inclusion coincide.