Fixed-Point Definability and Polynomial Time

13 years 6 months ago
Fixed-Point Definability and Polynomial Time
My talk will be a survey of recent results about the quest for a logic capturing polynomial time. In a fundamental study of database query languages, Chandra and Harel [4] first raised the question of whether there exists a logic that captures polynomial time. Actually, Chandra and Harel phrased the question in a somewhat disguised form; the version that we use today goes back to Gurevich [15]. Briefly, but slightly imprecisely,1 a logic L captures a complexity class K if exactly those properties of finite structures that are decidable in K are definable in L. The existence of a logic capturing PTIME is still wide open, and it is viewed as one of the main open problems in finite model theory and database theory. One reason the question is interesting is that we know from Fagin's Theorem [9] that existential second-order logic captures NP, and we also know that there are logics capturing most natural complexity classes above NP. Gurevich conjectured that there is no logic capturing...
Martin Grohe
Added 16 Aug 2010
Updated 16 Aug 2010
Type Conference
Year 2009
Where CSL
Authors Martin Grohe
Comments (0)