Formal Theories for Logspace Counting
Lila Fontes
TL;DR
This paper develops formal logical theories for the complexity classes ParityL and DET, capturing their computational power and reasoning principles related to problems like determinants over GF(2) and Z.
Contribution
It introduces two-sorted theories that precisely formalize reasoning within ParityL and DET, linking logical frameworks to these complexity classes.
Findings
Theories formalize reasoning about determinants over GF(2) and Z.
Definable functions in these theories match the classes' functions.
Provides a logical foundation for complexity classes ParityL and DET.
Abstract
We introduce two-sorted theories in the style of Cook and Nguyen for the complexity classes ParityL and DET, whose complete problems include determinants over GF(2) and Z, respectively. The definable functions in these theories are the functions in the corresponding complexity classes; thus each theory formalizes reasoning using concepts from its corresponding complexity class.
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Taxonomy
TopicsComplexity and Algorithms in Graphs · Advanced Graph Theory Research · Logic, Reasoning, and Knowledge