NDLI: On the equivalence and containment problems for unambiguous regular expressions, grammars, and automata

Content Provider	IEEE Xplore Digital Library
Author	Stearns, Richard E. Hunt, Harry B.
Copyright Year	1981
Abstract	The known proofs that the equivalence and containment problems for the regular and for the linear context-free grammars are PSPACE-complete and undecidable, respecitvely, depend upon consideration of ambiguous grammars. We prove that this dependence is inherent. Deterministic polynomial time algorithms are presented for; (1) the equivalence and containment problems for the unambiguous regular grammars; (2) for all k ≥ 2, the equivalence and containment problems for the regular grammars of degree of ambiguity ≤ k; and (3) the problems of determining if an unambiguous linear context-free grammar is equivalent to or contains an arbitrary regular set. Simple extensions of the grammar classes in (1), (2), and (3) are shown to yield problems that are NP-hard or undecidable. Several new results on the relative economy of description of ambiguous versus unambiguous regular and linear contextfree grammars are also obtained. These results depend upon several observations on the solutions of systems of homogeneous linear difference equations and their relationship with the number of strings of a given length generated by an unambiguous regular or linear context-free grammar.
Starting Page	74
Ending Page	81
File Size	1128889
Page Count	8
File Format	PDF
ISSN	02725428
DOI	10.1109/SFCS.1981.29
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1981-10-28
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Automata Polynomials Difference equations Computer science Terminology Gold Samarium
Content Type	Text
Resource Type	Article

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