Devising an efficient deterministic – or even a nondeterministic sub-exponential time – algorithm for testing polynomial identities is a fundamental problem in algebraic comp...
Modifying the methods of Z. Adamowicz's paper Herbrand consistency and bounded arithmetic (Fund. Math. 171 (2002)), we show that there exists a number n such that m Sm (the u...
Common binary arithmetic operations such as addition/subtraction and multiplication suffer from O(n) carry propagation delay where n is the number of digits. Carry lookahead helps...
The paper considers a commonly used axiomatization of the classical propositional logic and studies how different axiom schemata in this system contribute to proof complexity of th...
—Real number calculations on elementary functions are remarkably difficult to handle in mechanical proofs. In this paper, we show how these calculations can be performed within a...