Hilbert's Tenth problem and NP-completeness of Boolean Syllogistic with unordered cartesian product
Domenico Cantone, Pietro Ursino
TL;DR
This paper establishes a connection between Hilbert's Tenth problem and the NP-completeness of Boolean Syllogistic with unordered Cartesian product, proving its computational difficulty.
Contribution
It introduces the NP-completeness of Boolean Syllogistic with unordered Cartesian product and relates it to Hilbert's Tenth problem, a novel complexity result.
Findings
BS with unordered Cartesian product is NP-complete
Decidability problem for BS relates to Hilbert's Tenth problem
Provides complexity classification for a logical fragment
Abstract
We relate the decidability problem for BS with unordered cartesian product with Hilbert's Tenth problem and prove that BS with unordered cartesian product is NP-complete.
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Taxonomy
TopicsAdvanced Algebra and Logic · Computability, Logic, AI Algorithms · Formal Methods in Verification