Relativizations comparing NP and exponential time
Information and Control
Relational queries computable in polynomial time
Information and Control
Almost every set in exponential time is P-bi-immune
Theoretical Computer Science
On the complexity of bounded-variable queries (extended abstract)
PODS '95 Proceedings of the fourteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
The complexity of relational query languages (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
The Quest for a Logic Capturing PTIME
LICS '08 Proceedings of the 2008 23rd Annual IEEE Symposium on Logic in Computer Science
A Logic for PTIME and a Parameterized Halting Problem
LICS '09 Proceedings of the 2009 24th Annual IEEE Symposium on Logic In Computer Science
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
ICDT'05 Proceedings of the 10th international conference on Database Theory
From Almost Optimal Algorithms to Logics for Complexity Classes via Listings and a Halting Problem
Journal of the ACM (JACM)
A parameterized halting problem
The Multivariate Algorithmic Revolution and Beyond
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
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In [9] Yuri Gurevich addresses the question whether there is a logic that captures polynomial time. He conjectures that there is no such logic. He considers a logic, we denote it by L≤, that allows to express precisely the polynomial time properties of structures; however, apparently, there is no algorithm "that given an L≤-sentence ϕ produces a polynomial time Turing machine that recognizes the class of models of ϕ." In [12] Nash, Remmel, and Vianu have raised the question whether one can prove that there is no such algorithm. They give a reformulation of this question in terms of a parameterized halting problem p-ACC≤ for nondeterministic Turing machines. We analyze the precise relationship between L≤ and p-ACC≤. Moreover, we show that p-ACC≤ is not fixed-parameter tractable if "P ≠ NP holds for all time constructible and increasing functions." A slightly stronger complexity theoretic hypothesis implies that L≤ does not capture polynomial time. Furthermore, we analyze the complexity of various variants of p-ACC≤ and address the construction problem associated with p-ACC≤.