Relational queries computable in polynomial time
Information and Control
A logic for reasoning about probabilities
Information and Computation - Selections from 1988 IEEE symposium on logic in computer science
Journal of Computer and System Sciences - 3rd Annual Conference on Structure in Complexity Theory, June 14–17, 1988
Representing and reasoning with probabilistic knowledge: a logical approach to probabilities
Representing and reasoning with probabilistic knowledge: a logical approach to probabilities
PP is as hard as the polynomial-time hierarchy
SIAM Journal on Computing
Infinitary logics and 0–1 laws
Information and Computation - Special issue: Selections from 1990 IEEE symposium on logic in computer science
Journal of Computer and System Sciences
Randomized algorithms
P = BPP if E requires exponential circuits: derandomizing the XOR lemma
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Implicit Definability and Infinitary Logic in Finite Model Theory
ICALP '95 Proceedings of the 22nd International Colloquium on Automata, Languages and Programming
A Linguistic Characterization of Bounded Oracle Computation and Probabilistic Polynomial Time
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
The complexity of relational query languages (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
Finite Model Theory and Its Applications (Texts in Theoretical Computer Science. An EATCS Series)
Finite Model Theory and Its Applications (Texts in Theoretical Computer Science. An EATCS Series)
Two theorems on random polynomial time
SFCS '78 Proceedings of the 19th Annual Symposium on Foundations of Computer Science
Probabilistic databases: diamonds in the dirt
Communications of the ACM - Barbara Liskov: ACM's A.M. Turing Award Winner
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We study probabilistic complexity classes and questions of derandomisation from a logical point of view. For each logic L we introduce a new logic BPL, bounded error probabilistic L, which is defined from L in a similar way as the complexity class BPP, bounded error probabilistic polynomial time, is defined from P. Our main focus lies on questions of derandomisation, and we prove that there is a query which is definable in BPFO, the probabilistic version of first-order logic, but not in Cω∞ω 8?, finite variable infinitary logic with counting. This implies that many of the standard logics of finite model theory, like transitive closure logic and fixed-point logic, both with and without counting, cannot be derandomised. We prove similar results for ordered structures and structures with an addition relation, showing that certain uniform variants of AC0 (bounded-depth polynomial sized circuits) cannot be derandomised. These results are in contrast to the general belief that most standard complexity classes can be derandomised. Finally, we note that BPIFP+C, the probabilistic version of fixedpoint logic with counting, captures the complexity class BPP, even on unordered structures.