Proceedings Article10.1109/LICS.1997.614957
Two-variable logic with counting is decidable
Erich Grädel,Martin Otto,Eric Rosen +2 more
- 29 Jun 1997
- pp 306-317
230
TL;DR: It is proved that the satisfiability and the finite satisfiability problems for C/sup 2/ are decidable.
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Abstract: We prove that the satisfiability and the finite satisfiability problems for C/sup 2/ are decidable. C/sup 2/ is first-order logic with only two variables in the presence of arbitrary counting quantifiers 3/sup /spl ges/m/,m/spl ges/1. It considerably extends L/sup 2/ plain first-order with only two variables, which is known to be decidable by a result of Mortimer's. Unlike L/sup 2/, C/sup 2/ does not have the finite model property.
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Egon Boerger,Erich Grädel,Yuri Gurevich +2 more
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TL;DR: The Undecidable Standard Classes for Pure Predicate Logic, a Treatise on the Transformation of the Classical Decision Problem, and some Results and Open Problems are presented.
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On the Decision Problem for Two-Variable First-Order Logic
TL;DR: In this paper, the complexity of the satisfiability problem for FO2 is shown to be NEXPTIME-complete, and it is shown that every satisfiable FO2-sentence has a model whose size is at most exponential in the size of the sentence.
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Random Graph Isomorphism
TL;DR: A straightforward linear time canonical labeling algorithm is shown to apply to almost all graphs, and any graph Y can be easily tested for isomorphism to X by an extremely naive linear time algorithm.
Describing Graphs: A First-Order Approach to Graph Canonization
Neil Immerman,Eric S. Lander,Eric S. Lander +2 more
- 01 Jan 1990
TL;DR: In this article, the authors considered the problem of what must be added to first-order logic plus least-fixed point to obtain exactly the polynomial-time properties of unordered graphs.
341
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