Valiant, Leslie (1973) Decision procedures for families of deterministic pushdown automata. PhD thesis, University of Warwick.

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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:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Machine theory
Date:	July 1973
Institution:	University of Warwick
Theses Department:	Department of Computer Science
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Paterson, Michael S.
Sponsors:	Science Research Council (Great Britain) (SRC)
Extent:	138 leaves
Language:	eng
Related URLs:	Related item in WRAP
URI:	http://wrap.warwick.ac.uk/id/eprint/34701

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