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Expressive power of existential first-order sentences of Büchi's sequential calculus
- Source :
-
Discrete Mathematics . Mar2005, Vol. 291 Issue 1-3, p155-174. 20p. - Publication Year :
- 2005
-
Abstract
- Abstract: The aim of this paper is to study the first-order theory of the successor, interpreted on finite words. More specifically, we are interested in the hierarchy based on quantifier alternations (or -hierarchy). It was known (J. Comput. Syst. Sci. 25 (1982) 360–375) that this hierarchy collapses at level 2, but the expressive power of the lower levels was not characterized effectively. We give a semigroup theoretic description of the expressive power of , the boolean combinations of existential formulas. We also give an -time algorithm to decide whether the language accepted by a deterministic n-state automaton is expressible by a first-order sentence (respectively, a -sentence). [Copyright &y& Elsevier]
- Subjects :
- *MATHEMATICAL analysis
*MACHINE theory
*FORMAL languages
*PERMUTATIONS
Subjects
Details
- Language :
- English
- ISSN :
- 0012365X
- Volume :
- 291
- Issue :
- 1-3
- Database :
- Academic Search Index
- Journal :
- Discrete Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 17450105
- Full Text :
- https://doi.org/10.1016/j.disc.2004.04.027