We show that the term equivalence between MV-algebras and MV-semirings lifts to involutive residuated lattices a class of semirings called semirings. The semiring perspective leads necessary sufficient condition for interval [Formula: see text] be subalgebra an lattice, where is dualizing element. also import some results techniques semimodule theory in study this semirings, generalizing about ...

Formal power series over non-commuting variables have been investigated as representations of the behavior of automata with multiplicities. Here we introduce and investigate the concepts of aperiodic and of star-free formal power series over semirings and partially commuting variables. We prove that if the semiring K is idempotent and commutative, or if K is idempotent and the variables are non...

We claim that divisible residuated lattices (DRLs) can act as a unifying evaluation framework for soft constraint satisfaction problems (soft CSPs). DRLs form the algebraic semantics of a large family of substructural and fuzzy logics [13, 15], and are therefore natural candidates for this role. As a preliminary evidence in support to our claim, along the lines of Cooper et al. and Larrosa et a...

We will describe the recognizable formal power series over arbitrary semirings and in partially commuting variables, i.e. over trace monoids. We prove that the recognizable series are certain rational power series, which can be constructed from the polynomials by using the operations sum, product and a restricted star which is applied only to series for which the elements in the support all hav...

Weighted tree grammars (for short: WTG) are an extension of weighted context-free grammars that generate trees instead of strings. They can be used in natural language parsing to directly generate the parse tree of a sentence or to encode the set of all parse trees of a sentence. Two types of simulations for WTG over idempotent, commutative semirings are introduced. They generalize the existing...

Five algebraic notions of termination are formalised, analysed and compared: well-foundedness or Noetherity, Löb’s formula, absence of infinite iteration, absence of divergence and normalisation. The study is based on modal semirings, which are additively idempotent semirings with forward and backward modal operators. To reason about infinite behaviour, semirings are extended to divergence semi...

We give a general formula relating self cup products in cohomology to connecting maps in nonabelian cohomology, and apply it to obtain a formula for the self cup product associated to the Weil pairing.

In this paperwe adapt thewell-knownBrzozowskideterminizationmethod to fuzzy automata. Thismethod gives better results than all previously knownmethods for determinization of fuzzy automata developed by Bělohlávek [InformSciences 143 (2002)205–209],Li andPedrycz [FuzzySet Syst 156 (2005)68–92], Ignjatović et al. [Inform Sciences 178 (2008) 164–180], and Jančić et al. [Inform Sciences 181 (2011) ...

Weighted labelled transition systems are LTSs whose transitions are given weights drawn from a commutative monoid. WLTSs subsume a wide range of LTSs, providing a general notion of strong (weighted) bisimulation. In this paper we extend this framework towards other behavioural equivalences, by considering semirings of weights. Taking advantage of this extra structure, we introduce a general not...

We will describe the recognizable formal power series over arbitrary semirings and in partially commuting variables, i.e. over trace monoids. We prove that the recognizable series are certain rational power series, which can be constructed from the polynomials by using the operations sum, product and a restricted star which is applied only to series for which the elements in the support all hav...