The polynomial hierarchy and intuitionistic bounded arithmetic
Proc. of the conference on Structure in complexity theory
Bounded linear logic: a modular approach to polynomial-time computability
Theoretical Computer Science
Games and full completeness for multiplicative linear logic
Journal of Symbolic Logic
Bounded arithmetic, propositional logic, and complexity theory
Bounded arithmetic, propositional logic, and complexity theory
Information and Computation
Intrinsic Theories and Computational Complexity
LCC '94 Selected Papers from the International Workshop on Logical and Computational Complexity
An arithmetic for non-size-increasing polynomial-time computation
Theoretical Computer Science - Implicit computational complexity
Propositional computability logic I
ACM Transactions on Computational Logic (TOCL)
Propositional computability logic II
ACM Transactions on Computational Logic (TOCL)
Theoretical Computer Science - Clifford lectures and the mathematical foundations of programming semantics
An arithmetic for polynomial-time computation
Theoretical Computer Science - Clifford lectures and the mathematical foundations of programming semantics
From truth to computability II
Theoretical Computer Science
Intuitionistic computability logic
Acta Cybernetica
Sequential operators in computability logic
Information and Computation
Journal of Logic and Computation
On abstract resource semantics and computability logic
Journal of Computer and System Sciences
Toggling operators in computability logic
Theoretical Computer Science
A logical basis for constructive systems
Journal of Logic and Computation
Toggling operators in computability logic
Theoretical Computer Science
The taming of recurrences in computability logic through cirquent calculus, Part I
Archive for Mathematical Logic
A PSPACE-complete first-order fragment of computability logic
ACM Transactions on Computational Logic (TOCL)
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''Clarithmetic'' is a generic name for formal number theories similar to Peano arithmetic, but based on computability logic instead of the more traditional classical or intuitionistic logics. Formulas of clarithmetical theories represent interactive computational problems, and their ''truth'' is understood as existence of an algorithmic solution. Imposing various complexity constraints on such solutions yields various versions of clarithmetic. The present paper introduces a system of clarithmetic for polynomial time computability, which is shown to be sound and complete. Sound in the sense that every theorem T of the system represents an interactive number-theoretic computational problem with a polynomial time solution and, furthermore, such a solution can be efficiently extracted from a proof of T. And complete in the sense that every interactive number-theoretic problem with a polynomial time solution is represented by some theorem T of the system. The paper is written in a semitutorial style and targets readers with no prior familiarity with computability logic.