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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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01 Jan 2003
TL;DR: In this paper, the authors investigated the descriptional complexity of deterministic two-way k-head finite automata (k- DHA) and showed that for any k-DHA, k ≥ 2, there are savings in the size of description which cannot be bounded by any recursive function.
Abstract: We investigate the descriptional complexity of deterministic two-way k-head finite automata (k- DHA). It is shown that between non-deterministic pushdown automata and any k-DHA, k ≥ 2, there are savings in the size of description which cannot be bounded by any recursive function. The same is true for the other end of the hierarchy. Such non-recursive trade-offs are also shown between any k-DHA, k ≥ 1, and DSPACE(log) = multi-DHA. We also address the particular case of unary languages. In general, it is possible that non-recursive trade-offs for arbitrary languages reduce to recursive trade-offs for unary languages. Here we present huge lower bounds for the unary trade-offs between non-deterministic finite automata and any k-DHA, k ≥ 2. Furthermore, several known simulation results imply the presented trade-offs for other descriptional systems, e.g., deterministic two-way finite automata with k pebbles or with k linearly bounded counters.
14 citations
16 Jul 1979
TL;DR: Every strict deterministic language is generated by some injective controlled rewriting system iterating from a finite set of words, as improved on P. Butzbach's result.
Abstract: A controlled rewriting system over an alphabet X is a finite set of rules vi → wi (l⩽i⩽n) with vi , wi in X* such that |vi|<|wi| , each rule being associated with a regular language Ri X* Given such a system, f ⇒ g means that f=αviβ and g=αwiβ for some i, α in Ri , β in X* The system is said to be injective if and only if f ⇒ g ⇐ f′ implies f=f′ Controlled rewriting systems are a special case of finite relations with computable left context (P Butzbach [5], 1973), which can be defined as above, with the Ri's recursive instead of regular P Butzbach proved [5] that every simple deterministic language [11] is generated by some finite relation with computable left context iterating from a finite set of words Here we improve this result with our THEOREM 1 : "Every strict deterministic language is generated by some injective controlled rewriting system iterating from a finite set of words" Moreover, let A be a deterministic pushdown automaton and ⇒ be the rewriting relation associated with A by the above theorem Let θ : X* ⇒ X* defined by θ(u)=v if
and ∃ w, w ⇒ v (v is unique, for ⇒ is injective); in some sense, θ generalizes the semi-Dyck simplification We state :
14 citations
TL;DR: It is shown that model-checking past pushdown timed automata against Presburger safety properties on discrete clocks and stack word counts is decidable, and the reachability problem for a class of transition systems under some fairness constraints in the form of generalized past formulas is investigated.
14 citations
13 Dec 2004
TL;DR: An inherent relation between input-reversal pushdown automata and controlled linear context-free languages are shown, leading to an alternative description of Khabbaz geometric hierarchy of languages by input- reversal iterated push down automata.
Abstract: Input-reversal pushdown automata are pushdown automata with the additional power to reverse the unread part of the input. We show that these machines characterize the family of linear context-free indexed languages, and that k + 1 input reversals are better than k for both deterministic and nondeterministic input-reversal pushdown automata, i.e., there are languages which can be recognized by a deterministic input-reversal pushdown automaton with k + 1 input reversals but which cannot be recognized with k input reversals (deterministic or nondeterministic). In passing, input-reversal finite automata are investigated. Moreover, an inherent relation between input-reversal pushdown automata and controlled linear context-free languages are shown, leading to an alternative description of Khabbaz geometric hierarchy of languages by input-reversal iterated pushdown automata. Finally, some computational complexity problems for the investigated language families are considered.
14 citations
TL;DR: Hierarchies of automata operating on two-dimensional tapes are investigated and it is shown that finite automata with n+3 markers (n+2 heads) are strictly more powerful than those with n markers ( n heads).
Abstract: Hierarchies of automata operating on two-dimensional tapes are investigated. In particular, it is shown that finite automata with n+3 markers (n+2 heads) are strictly more powerful than those with n markers (n heads)
14 citations