Pushdown automaton

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

From security protocols to pushdown automata

Abstract: Formal methods have been very successful in analyzing security protocols for reachability properties such as secrecy or authentication In contrast, there are very few results for equivalence-based properties, crucial for studying eg privacy-like properties such as anonymity or vote secrecy We study the problem of checking equivalence of security protocols for an unbounded number of sessions Since replication leads very quickly to undecidability (even in the simple case of secrecy), we focus on a limited fragment of protocols (standard primitives but pairs, one variable per protocol's rules) for which the secrecy preservation problem is known to be decidable Surprisingly, this fragment turns out to be undecidable for equivalence Then, restricting our attention to deterministic protocols, we propose the first decidability result for checking equivalence of protocols for an unbounded number of sessions This result is obtained through a characterization of equivalence of protocols in terms of equality of languages of (generalized, real-time) deterministic pushdown automata

On the complexity of membership and counting in height-deterministic pushdown automata

Abstract: Visibly pushdown languages properly generalize regular languages and are properly contained in deterministic context-free languages. The complexity of their membership problem is equivalent to that of regular languages. However, the corresponding counting problem - computing the number of accepting paths in a visibly pushdown automaton - could be harder than counting paths in a non-deterministic finite automaton: it is only known to be in LogDCFL. We investigate the membership and counting problems for generalizations of visibly pushdown automata, defined using the notion of height-determinism. We show that, when the stack-height of a given pushdown automaton can be computed using a finite transducer, both problems have the same complexity as for visibly pushdown languages. We also show that when allowing pushdown transducers instead of finite-state ones, both problems become LogDCFL-complete; this uses the fact that pushdown transducers are sufficient to compute the stack heights of all real-time height-deterministic pushdown automata, and yields a candidate arithmetization of LogDCFL that is no harder than LogDCFL (our main result).

Reachability problem for weak multi-pushdown automata

Abstract: This paper is about reachability analysis in a restricted subclass of multi-pushdown automata: we assume that the control states of an automaton are partially ordered, and all transitions of an automaton go downwards with respect to the order. We prove decidability of the reachability problem, and computability of the backward reachability set. As the main contribution, we identify relevant subclasses where the reachability problem becomes NP-complete. This matches the complexity of the same problem for communication-free vector addition systems (known also as commutative context-free graphs), a special case of stateless multi-pushdown automata.