Diagonalization in proof complexity

Diagonalization in proof complexity

Relations Between Diagonalization, Proof Systems, and Complexity Gaps

In this paper we study diagonal processes over time bounded computations of one-tape Turing machines by diagonalizing only over those machines for which there exist formal pro& that they operate in the given time bound. This replaces the traditional “clock” jr. .-zsource bounded diagonalization by formal proofs about running times and establishes close relations between properties of proof syst...

The Mechanization of the Diagonalization Proof StrategyLassaad

We present an empirical study of mathematical proofs by diagonalization, the aim is their mechanization based on proof planning techniques. We show that these proofs can be constructed according to a strategy that (i) nds an indexing relation, (ii) constructs a diagonal element, and (iii) makes the implicit contradiction of the diagonal element explicit. Moreover we suggest how diagonal element...

Space in Proof Complexity

Propositional proof complexity is the study of the resources that are needed to prove formulas in propositional logic. In this thesis we are concerned with the size and space of proofs, and in particular with the latter. There are different approaches to reasoning that are captured by corresponding proof systems, each with its own strengths and weaknesses and need for resources. The simplest an...

The Invalidity of Diagonalization Proof for Halting Problem

We examine the converse of Church-Turing thesis and establish the existence of uncountable number of accelerated Turing machines. This leads to the case that these machines are unaffected by Gödel’s incompleteness