Valiant, Leslie (1973) Decision procedures for families of deterministic pushdown automata. University of Warwick. Department of Computer Science. (Theory of Computation Report). (Unpublished)

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Abstract

The existence and complexity of decision procedures for families of deterministic pushdown automata are investigated, with special emphasis on positive decidability results for those questions, such as equivalence, which are known to become undecidable when the deterministic restriction is removed. The equivalence problem is proved decidable for the following three deterministic families, all of which are already extensive enough to have undecidable inclusion problems: (a) nonsingular automata - a realtime subfamily, which extends the largest corresponding classes with previously known equivalence tests, (b) finite-turn automata - characterised by having a bound on the number of times the direction of the stack movement can change, and (c) one-counter automata - defined by restricting the stack alphabet to just one symbol. The problem of whether a language defined by a machine in one family, can be recognised by one in another, is a convenient formulation of numerous decidable or potentially decidable questions. We show that such questions as whether a deterministic context-free language can be recognised by a machine in any one of the above named classes, must be, if decidable at all, at least as difficult to decide as whether such a language is regular. We re-examine the regularity test of Stearns, and obtain an improved algorithm. We do this by reducing by an exponential order the upper bound on the possible state complexity of regular sets recognised by deterministic pushdown automata of a given size, to a level close to one known to be achievable. We pursue an application of this analysis to a schema theoretic problem. We consider the succinctness with which certain functional schemas can be used to express equivalent large flowchart schemas, and obtain closely matching upper and lower bounds for a measure of this.

Item Type:	Report
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Computer Science
Library of Congress Subject Headings (LCSH):	Machine theory
Series Name:	Theory of Computation Report
Publisher:	University of Warwick. Department of Computer Science
Official Date:	August 1973
Dates:	Date Event August 1973 ["eprint_fieldopt_dates_date_type_available" not defined]
Number:	Number 1
Number of Pages:	140
DOI:	CS-RR-001
Institution:	University of Warwick
Theses Department:	Department of Computer Science
Status:	Not Peer Reviewed
Publication Status:	Unpublished
Access rights to Published version:	Open Access (Creative Commons)
Description:	See Related URL for option to download full text
Version or Related Resource:	Valiant, L.G. (1973). Decision procedures for families of deterministic pushdown automata. Ph.D. thesis. University of Warwick
Related URLs:	Related item in WRAP

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