The max-Łukasiewicz semiring is defined as the unit interval [0, 1] equipped with the arithmetics “a + b” = max(a, b) and “ab” = max(0, a + b− 1). Linear algebra over this semiring can be developed in the usual way. We observe that any problem of the max-Łukasiewicz linear algebra can be equivalently formulated as a problem of the tropical (max-plus) linear algebra. Based on this equivalence, w...

Many “semiring-like” structures are used in Soft Constraint Satisfaction Problems (SCSPs). We review a few properties of semirings that are useful for dealing with soft constraints, highlighting the differences between alternative proposals in the literature. We then extend the semiring structure by adding the notion of division as a weak inverse operation of product. In particular, division is...

This paper proposes a semiring formulation for reasoning about an agent’s changing beliefs: a dynamic epistemic semiring (DES). A DES is a modal semiring extended with a revision operator. The revision operator is given a relational interpretation and a basic calculus is developed – based on the revision operator a contraction operator is also defined. A DES only models actions on an agent’s be...

decorations of parse forests usingdynamic programming and algebraicpower series. Theoretical Computer Science.To appear.Tendeau, Frédéric. 1997b. An Earleyalgorithm for generic attribute augmentedgrammars and applications. In Proceedingsof the International Workshop on ParsingTechnologies 1997, pages 199–209.Viterbi, Andrew J. 1967. Error bounds forconvol...

Digital signatures are probably the most important and widely used cryptographic primitive enabled by public key technology, and they are building blocks of many modern distributed computer applications, like, electronic contract signing, certified email, and secure web browsing etc. But many existing signatures schemes lie in the intractability of problems closely related to the number theory ...

Let S be a complete star-omega semiring and Σ be an alphabet. For a weighted ω-pushdown automaton P with stateset {1, . . . ,n}, n ≥ 1, we show that there exists a mixed algebraic system over a complete semiring-semimodule pair ((S≪ Σ ≫),(S≪ Σ ≫)) such that the behavior ‖P‖ of P is a component of a solution of this system. In case the basic semiring is B or N we show that there exists a mixed c...

For functions defined on Cn or Rn+ we construct a dequantization transform f 7→ f̂ ; this transform is closely related to the Maslov dequantization. If f is a polynomial, then the subdifferential ∂f̂ of f̂ coincides with the Newton polytope of f . For the semiring of polynomials with nonnegative coefficients, the dequantization transform is a homomorphism of this semiring to the idempotent semirin...

For functions defined on C or R+ we construct a dequantization transform f 7→ f̂ ; this transform is closely related to the Maslov dequantization. If f is a polynomial, then the subdifferential ∂f̂ of f̂ at the origin coincides with the Newton polytope of f . For the semiring of polynomials with nonnegative coefficients, the dequantization transform is a homomorphism of this semiring to the idempo...

In this paper we introduce a novel use of the lexicographic semiring and motivate its use for speech and language processing tasks. We prove that the semiring allows for exact encoding of backoff models with epsilon transitions. This allows for off-line optimization of exact models represented as large weighted finite-state transducers in contrast to implicit (on-line) failure transition repres...

We introduce two generalizations of synchronizability to automata with transitions weighted in an arbitrary semiring K = (K,+, ·,0,1). For states p,q and word u, let (pu)q ∈ K denote the sum of the weights of all u-labeled paths from p to q, with the weigth of a path being the product of the weights of its edges, as usual. We call the automaton A location-synchronizable if ∃q,u: ∀p,r (pu)r 6= 0...