Pushdown automaton

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

On the computational complexity of algebraic numbers: the Hartmanis--Stearns problem revisited

Abstract: — We consider the complexity of integer base expansions of algebraic irrational numbers from a computational point of view. We show that the Hartmanis–Stearns problem can be solved in a satisfactory way for the class of multistack machines. In this direction, our main result is that the base-b expansion of an algebraic irrational real number cannot be generated by a deterministic pushdown automaton. We also confirm an old claim of Cobham proving that such numbers cannot be generated by a tag machine with dilation factor larger than one.

Logics for Weighted Timed Pushdown Automata

Abstract: Weighted dense-timed pushdown automata with a timed stack were introduced by Abdulla, Atig and Stenman to model the behavior of real-time recursive systems. Motivated by the decidability of the optimal reachability problem for weighted timed pushdown automata and weighted logic of Droste and Gastin, we introduce a weighted MSO logic on timed words which is expressively equivalent to weighted timed pushdown automata. To show the expressive equivalence result, we prove a decomposition theorem which establishes a connection between weighted timed pushdown languages and visibly pushdown languages of Alur and Mudhusudan; then we apply their result about the logical characterization of visibly pushdown languages.

Non-Self-Embedding Grammars, Constant-Height Pushdown Automata, and Limited Automata

Abstract: Non-self-embedding grammars are a restriction of context-free grammars which does not allow to describe recursive structures and, hence, which characterizes only the class of regular languages. A double exponential gap in size from non-self-embedding grammars to deterministic finite automata is known. The same size gap is also known from constant-height pushdown automata and 1-limited automata to deterministic finite automata. Constant-height pushdown automata and 1-limited automata are compared with non-self-embedding grammars. It is proved that non-self-embedding grammars and constant-height pushdown automata are polynomially related in size. Furthermore, a polynomial size simulation by 1-limited automata is presented. However, the converse transformation is proved to cost exponential.

On the size of DASG for multiple texts

Abstract: We present a left-to-right algorithm building the automaton accepting all subsequences of a given set of strings. We prove that the number of states of this automaton can be quadratic if built on at least two texts.

On the membership problem for visibly pushdown languages

Abstract: Visibly pushdown languages are a subclass of deterministic context-free languages that can model nonregular properties of interest in program analysis. This class properly contains typical classes of parenthesized languages like “balanced” and “input-driven” languages. Visibly pushdown languages are closed under boolean operations and some decision problems, such as inclusion and universality, are decidable. In this paper, we study the membership problem for this class of languages and show that it can be solved in time linear in the size of the input grammar and in the length of the input word. The algorithm consists of a reduction to the reachability problem on game graphs. The same approach can be efficiently applied when the input language is given as a visibly pushdown automaton, moreover we also show time complexities of the same problem using other approaches. We further motivate our result showing an application to XML schema.