Semirings, automata, languages
Semirings, automata, languages
Torsion matrix semigroups and recognizable transductions
International Colloquium on Automata, Languages and Programming on Automata, languages and programming
Theory of linear and integer programming
Theory of linear and integer programming
Notes on logic and set theory
Algorithms for determining relative star height and star height
Information and Computation
Relative star height, star height and finite automata with distance functions
Proceedings of the LITP Spring School on Theoretical Computer Science on Formal properties of finite automata and applications
Complete systems of B -rational identities
Theoretical Computer Science
Selected papers of the second international colloquium on Words, languages and combinatorics
Recognizable Sets with Multiplicities in the Tropical Semiring
MFCS '88 Proceedings of the Mathematical Foundations of Computer Science 1988
Methods and Applications of (MAX, +) Linear Algebra
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
An algebraic method for solving decision problems in finite automata theory
An algebraic method for solving decision problems in finite automata theory
Axiomatizing rational power series over natural numbers
Information and Computation
Enhancing constraints manipulation in semiring-based formalisms
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
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This paper studies the equational theories of various exotic semirings presented in the literature. Exotic semirings are semirings whose underlying carrier set is some subset of the set of real numbers equipped with binary operations of minimum or maximum as sum, and addition as product. Two prime examples of such structures are the (max,+) semiring and the tropical semiring. It is shown that none of the exotic semirings commonly considered in the literature has a finite basis for its equations, and that similar results hold for the commutative idempotent weak semirings that underlie them. For each of these commutative idempotent weak semirings, the paper offers characterizations of the equations that hold in them, decidability results for their equational theories, explicit descriptions of the free algebras in the varieties they generate, and relative axiomatization results.