The method of forced enumeration for nondeterministic automata
Acta Informatica
The expressive power of second order Horn logic
STACS 91 Proceedings of the 8th annual symposium on Theoretical aspects of computer science
Capturing complexity classes by fragments of second-order logic
Theoretical Computer Science - Special issue on logic and applications to computer science
Bounded arithmetic, propositional logic, and complexity theory
Bounded arithmetic, propositional logic, and complexity theory
Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
The complexity of relational query languages (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Relational queries computable in polynomial time (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Feasibly constructive proofs and the propositional calculus (Preliminary Version)
STOC '75 Proceedings of seventh annual ACM symposium on Theory of computing
Languages which capture complexity classes
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
A Second-Order System for Polytime Reasoning Using Grädel's Theorem
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Fixed-point logics, descriptive complexity, and random satisfiability
Fixed-point logics, descriptive complexity, and random satisfiability
Systems of bounded arithmetic from descriptive complexity
Systems of bounded arithmetic from descriptive complexity
Closure properties of weak systems of bounded arithmetic
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
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There are many ways to define complexity in logic. In finite model theory, it is the complexity of describing properties, whereas in proof complexity it is the complexity of proving properties in a proof system. Here we consider several notions of complexity in logic, the connections among them, and their relationship with computational complexity. In particular, we show how the complexity of logics in the setting of finite model theory is used to obtain results in bounded arithmetic, stating which functions are provably total in certain weak systems of arithmetic. For example, the transitive closure function (testing reachability between two given points in a directed graph) is definable using only NL-concepts (where NL is non-deterministic log-space complexity class), and its totality is provable within NL-reasoning.