Journal of Symbolic Logic 67 (3):1093-1125 (2002)
|Abstract||This paper is motivated by the question whether there exists a logic capturing polynomial time computation over unordered structures. We consider several algorithmic problems near the border of the known, logically defined complexity classes contained in polynomial time. We show that fixpoint logic plus counting is stronger than might be expected, in that it can express the existence of a complete matching in a bipartite graph. We revisit the known examples that separate polynomial time from fixpoint plus counting. We show that the examples in a paper of Cai, Fürer, and Immerman, when suitably padded, are in choiceless polynomial time yet not in fixpoint plus counting. Without padding, they remain in polynomial time but appear not to be in choiceless polynomial time plus counting. Similar results hold for the multipede examples of Gurevich and Shelah, except that their final version of multipedes is, in a sense, already suitably padded. Finally, we describe another possible candidate, involving determinants, for the task of separating polynomial time from choiceless polynomial time plus counting|
|Keywords||No keywords specified (fix it)|
|Through your library||Configure|
Similar books and articles
Maria Bulińska (2009). On the Complexity of Nonassociative Lambek Calculus with Unit. Studia Logica 93 (1).
Erik Aarts (1994). Proving Theorems of the Second Order Lambek Calculus in Polynomial Time. Studia Logica 53 (3):373 - 387.
Yuri Gurevich & Saharon Shelah (1989). Time Polynomial in Input or Output. Journal of Symbolic Logic 54 (3):1083-1088.
Martin Otto (1996). The Expressive Power of Fixed-Point Logic with Counting. Journal of Symbolic Logic 61 (1):147-176.
Douglas Cenzer & Jeffrey B. Remmel (2006). Complexity, Decidability and Completeness. Journal of Symbolic Logic 71 (2):399 - 424.
Natacha Portier (2000). Le Problème Des granDes Puissances Et Celui Des granDes Racines. Journal of Symbolic Logic 65 (4):1675-1685.
Thomas Strahm (1997). Polynomial Time Operations in Explicit Mathematics. Journal of Symbolic Logic 62 (2):575-594.
Stephen A. Fenner, Stuart A. Kurtz & James S. Royer (2004). Every Polynomial-Time 1-Degree Collapses If and Only If P = Pspace. Journal of Symbolic Logic 69 (3):713-741.
Lauri Hella (1996). Logical Hierarchies in PTIME. Information and Computation 129 (1):1--19.
Andreas Blass & Yuri Gurevich (2003). Strong Extension Axioms and Shelah's Zero-One Law for Choiceless Polynomial Time. Journal of Symbolic Logic 68 (1):65-131.
Added to index2009-01-28
Total downloads3 ( #201,781 of 549,037 )
Recent downloads (6 months)0
How can I increase my downloads?