Weighted Rewriting: Semiring Semantics for Abstract Reduction Systems
Year: 2025
Type: preprint
Abstract: We present novel semiring semantics for abstract reduction systems (ARSs). More precisely, we provide a weighted version of ARSs, where the reduction steps induce weights from a semiring. Inspired by provenance analysis in database theory and logic, we obtain a formalism that can be used for provenance analysis of arbitrary ARSs. Our semantics handle (possibly unbounded) non-determinism and possibly infinite reductions. Moreover, we develop several techniques to prove upper and lower bounds on the weights resulting from our semantics, and show that in this way one obtains a uniform approach to analyze several different properties like termination, derivational complexity, space complexity, safety, as well as combinations of these properties.
Source: arXiv (Cornell University)
Authors: Ahrens, Emma, Kassing, Jan-Christoph, Giesl, Jürgen, Katoen, Joost-Pieter
Institution: RWTH Aachen University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6966747319
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