CSE200: Computability and complexity Interactive proofs

CSE200: Computability and complexity Randomized algorithms

The Computational Complexity of Propositional Cirquent Calculus

Introduced in 2006 by Japaridze, cirquent calculus is a refinement of sequent calculus. The advent of cirquent calculus arose from the need for a deductive system with a more explicit ability to reason about resources. In particular, cirquent calculus has been instrumental in axiomatizing various fundamental fragments of Computability Logic, a formal theory of (interactive) computability. The s...

Kolmogorov Complexity Theory over the Reals

Kolmogorov Complexity constitutes an integral part of computability theory, information theory, and computational complexity theory— in the discrete setting of bits and Turing machines. Over real numbers, on the other hand, the BSS-machine (aka real-RAM) has been established as a major model of computation. This real realm has turned out to exhibit natural counterparts to many notions and resul...

On the system CL12 of computability logic

Computability logic (CoL) is a long-term project for redeveloping logic on the basis of a constructive game semantics, with games seen as abstract models of interactive computational problems. Among the fragments of CoL successfully axiomatized so far is CL12 — a conservative extension of classical first-order logic, whose language augments that of classical logic with the so called choice (“co...

Introduction to clarithmetic II

The earlier paper " Introduction to clarithmetic I " constructed an axiomatic system of arithmetic based on computability logic, and proved its soundness and extensional completeness with respect to polynomial time computability. The present paper elaborates three additional sound and complete systems in the same style and sense: one for polynomial space computability, one for elementary recurs...