The semiring-based formalism to model soft constraint has been introduced in 1995 by Ugo Montanari and the authors of this paper. The idea was to make constraint programming more flexible and widely applicable. We also wanted to define the extension via a general formalism, so that all its instances could inherit its properties and be easily compared. Since then, much work has been done to stud...

From now on X denotes a set and S denotes a family of subsets of X. Now we state the propositions: (1) Let us consider sets X1, X2, a family S1 of subsets of X1, and a family S2 of subsets of X2. Then {a×b, where a is an element of S1, b is an element of S2 : a ∈ S1 and b ∈ S2} = {s, where s is a subset of X1 ×X2 : there exist sets a, b such that a ∈ S1 and b ∈ S2 and s = a × b}. Proof: {a × b,...

The basic aim of key exchange is that two people who can only communicate via an insecure channel want to find a common secre t key without any attack. In this paper we show a model of key-agreement protocol using polynomials over non-commutative division semiring for network security. It is proved that the proposed protocol meets several security attributes under the assumption that the polyno...

We investigate the theory of skew (formal) power series introduced by Droste, Kuske [4, 5], if the basic semiring is a Conway semiring. This yields Kleene Theorems for skew power series, whose supports contain finite and infinite words. We then develop a theory of convergence in semirings of skew power series based on the discrete convergence. As an application this yields a Kleene Theorem prov...

The problem of computing the edit-distance between a string and a finite automaton arises in a variety of applications in computational biology, text processing, and speech recognition. This paper presents linear-space algorithms for computing the edit-distance between a string and an arbitrary weighted automaton over the tropical semiring, or an unambiguous weighted automaton over an arbitrary...

We investigate modal algebras that arise by adding operations of domain and antidomain to semirings and Kleene algebras. Let (S,+, ·, 0, 1) be a noncommutative and additively idempotent semiring with natural order defined as x ≤ y ⇔ x + y = x. Such semirings have many computational models, e.g., binary relations under union and relative product, languages, paths in graphs or program traces unde...

A general homomorphic overloading in a first-order type system is discussed. Type inference is applied within predefined classes each containing an arbitrary first-order subtyping hierarchy. We propose a computationally efficient type inference algorithm by converting the attendant constraint-satisfaction problem into the algebraic path problem for a constraint graph weighted with elements of a...

We present a variant of the Weighted Maximum Satisfiability Problem (Weighted Max-SAT), which is a modeling of the Semiring Constraint Satisfaction framework. We show how to encode a Semiring Constraint Satisfaction Problem (SCSP) into an instance of a propositional Weighted Max-SAT, and call the encoding Weighted Semiring Max-SAT (WS-Max-SAT). The clauses in our encoding are highly structured ...

We present a disambiguation algorithm for weighted automata. The algorithm admits two main stages: a pre-disambiguation stage followed by a transition removal stage. We give a detailed description of the algorithm and the proof of its correctness. The algorithm is not applicable to all weighted automata but we prove sufficient conditions for its applicability in the case of the tropical semirin...

Weighted automata map input words to values, and have numerous applications in computer science. A result by Krob from the 90s implies that universality problem is decidable for weighted over tropical semiring with weights N ? { ? } undecidable when are Z . We continue study of borders decidability semiring. give a complete picture complexity various decision problems them, including non-emptin...