Pushdown automata may contain transitions that are never used in any accepting run of the automaton. We present an algorithm for detecting such useless transitions. A finite automaton that captures the possible stack content during runs of the pushdown automaton, is first constructed in a forward procedure to determine which transitions are reachable, and then employed in a backward procedure t...

We apply a construction of Cook (1971) to show that the intersection nonemptiness problem for one PDA (pushdown automaton) and a finite list of DFA’s (deterministic finite automata) characterizes the complexity class P. In particular, we show that there exist constants c1 and c2 such that for every k, intersection non-emptiness for one PDA and k DFA’s is solvable in O(nc1k) time, but is not sol...

Two-way alternating automata on trees were introduced by Vardi [Va98]. Here we consider alternating two-way automata on graphs and show the decidability of the following problem: ,,does a given automaton with the Büchi condition accept any finite graph?” Using this result we demonstrate the decidability of the finite model problem for a certain fragment of the modal μ-calculus with backward mod...

We introduce and investigate input-driven stack automata, which are a generalization of input-driven pushdown automata that recently became popular under the name visibly pushdown automata. Basically, the idea is that the input letters uniquely determine the operations on the pushdown store. This can nicely be generalized to stack automata by further types of input letters which are responsible...

Higher-order pushdown systems generalize pushdown systems by using higher-order stacks, which are nested stacks of stacks. In this article, we consider parity games defined by higher-order pushdown systems and provide a k-Exptime algorithm to compute finite representations of positional winning strategies for both players for games defined by level-k higher-order pushdown automata. Our result i...

We deal with matching and locating of patterns in forests of variable arity. A pattern consists of a structural and a contextual condition for subtrees of a forest, both of which are given as tree or forest regular languages. We use the notation of constraint systems to uniformly specify both kinds of conditions. In order to implement pattern matching we introduce the class of pushdown forest a...

A one-counter automaton is a pushdown automaton over a singleton stack alphabet. We prove that the bisimilarity of processes generated by nondeterministic one-counter automata (with no ε-steps) is in PSPACE. This improves the previously known decidability result (Jančar 2000), and matches the known PSPACE lower bound (Srba 2009). We add the PTIME-completeness result for deciding regularity (i.e...

We investigate several unconventional models of finite automata and algorithms. We show that two-way alternating automata can be smaller than fast bounded-error probabilistic automata. We introduce ultrametric finite automata which use p-adic numbers to describe the branching process of the computation. We examine the size complexity of all the abovementioned automata for the counting problem. ...

We introduce a natural extension of collapsible pushdown systems called annotated pushdown systems that replaces collapse links with stack annotations. We believe this new model has many advantages. We present a saturation method for global backwards reachability analysis of these models that can also be used to analyse collapsible pushdown systems. Beginning with an automaton representing a se...