Pushdown automaton

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

Tree automata with memory, visibility and structural constraints

Abstract: Tree automata with one memory have been introduced in 2001. They generalize both pushdown (word) automata and the tree automata with constraints of equality between brothers of Bogaert and Tison. Though it has a decidable emptiness problem, the main weakness of this model is its lack of good closure properties. We propose a generalization of the visibly pushdown automata of Alur and Madhusudan to a family of tree recognizers which carry along their (bottom-up) computation an auxiliary unbounded memory with a tree structure (instead of a symbol stack). In other words, these recognizers, called visibly Tree Automata with Memory (VTAM) define a subclass of tree automata with one memory enjoying Boolean closure properties. We show in particular that they can be determinized and the problems like emptiness, inclusion and universality are decidable for VTAM. Moreover, we propose an extension of VTAM whose transitions may be constrained by structural equality and disequality tests between memories, and show that this extension preserves the good closure and decidability properties.

State complexity of operations on input-driven pushdown automata

Abstract: The family of deterministic input-driven pushdown automata (IDPDA; a.k.a. visibly pushdown automata, a.k.a. nested word automata) is known to be closed under reversal, concatenation and Kleene star. As shown by Alur and Madhusudan ("Visibly pushdown languages", STOC 2004), the reversal and the Kleene star of an n-state IDPDA can be represented by an IDPDA with 2O(n2) states, while concatenation of an m-state and an n-state IDPDA is represented by an IDPDA with 2O((m+n)2) states. This paper presents more efficient constructions for the reversal and for the Kleene star, which yield 2Θ(n log n) states, as well as an m2Θ(n log n)-state construction for the concatenation. These constructions are optimal due to the previously known matching lower bounds.

Discrete Asymptotic Abstractions of Hybrid Systems

Abstract: In this paper we introduce the notion of Finite Time Mode Abstraction to relate a hybrid automaton to a timed automaton that preserves the stability and reachability properties of the former. The abstraction procedure discards the continuous dynamics of each mode in the hybrid automaton completely, keeping only the information about the maximum time in which the continuous state makes a discrete jump. This information is used to construct a timed automaton, based on the original hybrid automaton, and to prove that the stability and reachability properties of the original system are retained in the abstract timed automaton. In the process of abstracting a hybrid to a timed automaton we introduce a new notion of hybrid distance metric, which provides information about both the number of discrete transitions that a system would have to make to go from one hybrid state to another, and the distance between the continuous parts of such hybrid states.

Notes on Pre-Set Pushdown Automata

Abstract: Motivated by practical implementation-methods for recursive program-schemata we will define and study presetting techniques for push-down automata. The main results will characterize the languages of preset pda's in terms of types of iterated substitution languages. In particular when conditions of "locally finiteness" and of "finite returning" are imposed we get a feasible machine-model for a class of developmental languages. The accepted family extends to the smallest AFL enclosing it when we drop the condition of locally finiteness. At the same time this family will be the smallest such full AFL. If all conditions are removed, present pda's exactly represent the family of iterated regular substitution languages, a sub-family of the indexed languages. Deterministic preset pda's are also studied, and the language-family they define is shown to be closed under complementation, generalizing a classical result.