TL;DR
This paper introduces a framework linking circuit complexity of Boolean functions to their polymorphisms, providing new characterizations for both deterministic and non-deterministic circuit complexities based on the functions' truth tables.
Contribution
It establishes a novel connection between circuit complexity and polymorphisms, extending techniques from CSP analysis to Boolean circuit complexity.
Findings
Circuit complexity characterized by partial polymorphisms.
Non-deterministic circuit complexity characterized by polymorphisms.
Framework inspired by CSP analysis techniques.
Abstract
We present a framework for studying circuit complexity that is inspired by techniques that are used for analyzing the complexity of CSPs. We prove that the circuit complexity of a Boolean function is characterized by the partial polymorphisms of 's truth table. Moreover, the non-deterministic circuit complexity of is characterized by the polymorphisms of 's truth table.
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Taxonomy
Topicssemigroups and automata theory · Machine Learning and Algorithms · Computability, Logic, AI Algorithms