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Pushdown automaton
About: Pushdown automaton is a research topic. Over the lifetime, 1868 publications have been published within this topic receiving 35399 citations.
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TL;DR: A fundamental framework of automata and grammars theory based on quantum logic is preliminarily established and it is showed that the language generated by any l valued regular grammar is equivalent to that recognized by some automaton with e moves based onquantum logic.
Abstract: In this paper, a fundamental framework of automata and grammars theory based on quantum logic is preliminarily established. First, the introduce quantum grammar, which is called l valued grammars, is introduced. It is particularly showed that the language (called quantum language) generated by any l valued regular grammar is equivalent to that recognized by some automaton with e moves based on quantum logic (called l valued automata), and conversely, any quantum language recognized by l valued automaton is also equivalent to that generated by some l valued grammar. Afterwards, the l valued pumping lemma is built, and then a decision characterization of quantum languages is presented. Finally, the relationship between regular grammars and quantum grammars (l valued regular grammars) is briefly discussed. Summarily, the introduced work lays a foundation for further studies on more complicated quantum automata and quantum grammars such as quantum pushdown automata and Turing machine as well as quantum context-free grammars and context-sensitive grammars.
15 citations
TL;DR: The result is used to show that the hierarchy of classes of languages accepted by pushdown automata based on the number of alternations collapses at the second level of the hierarchy.
Abstract: Languages accepted by alternating auxiliary pushdown automata using simultaneously a(n) alternations and s(n) space are shown to be members of the class of languages accepted by nondeterministic Turing machines using a(n) 2es(n) space for some c > 0. This result is used to show that the hierarchy of classes of languages accepted by pushdown automata based on the number of alternations collapses at the second level of the hierarchy. The power of alternation bounded pushdown automata without auxiliary storage is also investigated.
15 citations
TL;DR: A notion of a probabilistic tree automaton is defined and a condition is given under which it is equivalent to a usual tree Automaton, and a theorem about context free languages is stated.
Abstract: A notion of a probabilistic tree automaton is defined and a condition is given under which it is equivalent to a usual tree automaton. A theorem about context free languages is stated.
15 citations
TL;DR: The Chomsky-Schutzenberger Theorem is derived, showing that quantitative context-free languages are expressively equivalent to a model of weighted pushdown automata and that each arises as the image of the intersection of a Dyck language and a recognizable language under a suitable morphism.
Abstract: Weighted automata model quantitative aspects of systems like the consumption of resources during executions. Traditionally, the weights are assumed to form the algebraic structure of a semiring, but recently also other weight computations like average have been considered. Here, we investigate quantitative context-free languages over very general weight structures incorporating all semirings, average computations, lattices. In our main result, we derive the Chomsky-Schutzenberger Theorem for such quantitative context-free languages, showing that each arises as the image of the intersection of a Dyck language and a recognizable language under a suitable morphism. Moreover, we show that quantitative context-free languages are expressively equivalent to a model of weighted pushdown automata. This generalizes results previously known only for semirings. We also investigate under which conditions quantitative context-free languages assume only finitely many values.
15 citations
TL;DR: This work proposes a generalization of the visibly pushdown automata of Alur and Madhusu- dan 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).
Abstract: Tree automata with one memory have been introduced in 2001. They gener- alize 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 Madhusu- dan 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, member- ship, inclusion and universality are decidable for VTAM. Moreover, we propose several extensions of VTAM whose transitions may be constrained by different kinds of tests be- tween memories and also constraints a la Bogaert and Tison. We show that some of these classes of constrained VTAM keep the good closure and decidability properties, and we demonstrate their expressiveness with relevant examples of tree languages.
15 citations