We introduce and investigate a weighted propositional configuration logic over commutative semirings. Our is intended to serve as specification language for software architectures with quantitative features. prove an efficient construction of full normal forms decidability equivalence formulas in this logic. illustrate the motivation work by describing well-known equipped characteristics using ...

Let R be a commutative semiring with $ 1 \neq0$ . In this paper, we study the concept of weakly 1-absorbing primary ideal which is generalization overccommutative semirings A proper I called if whenever nonunit elements $a,b,c \in R$ and $0 \neq abc I$, then $ab $or $c \sqrt{I}$. number results concerning ideals examples are given. And need special type k-ideal or subtractive helps to prove rel...

We show that the validity of Parikh’s theorem for context-free languages depends only on a few equational properties of least pre-fixed points. Moreover, we exhibit an infinite basis of μ-term equations of continuous commutative idempotent semirings. AMS Subject Classification (2000): 03C05, 16Y60, 68Q42, 68Q45, 68Q70.

We consider a first-order logic, a linear temporal logic, star-free expressions and counter-free Büchi automata, with weights, over idempotent, zerodivisor free and totally commutative complete semirings. We show the expressive equivalence (of fragments) of these concepts, generalizing in the quantitative setup, the corresponding folklore result of formal language theory.

We prove an analog of Parikh’s theorem for weighted context-free grammars over commutative, idempotent semirings, and exhibit a stochastic context-free grammar with behavior that cannot be realized by any stochastic right-linear context-free grammar. Finally, we show that every unary stochastic context-free grammar with polynomially-bounded ambiguity has an equivalent stochastic right-linear co...

Tree series transformations computed by bottom-up tree series transducers are called bottom-up tree series transformations. (Functional) compositions of such transformations are investigated. It turns out that bottom-up tree series transformations over commutative and א0-complete semirings are closed under left-composition with linear bottom-up tree series transformations and right-composition ...

We introduce two partially overlapping classes of pathwise dualities between interacting particle systems that are based on commutative monoids (semigroups with a neutral element) and semirings, respectively. For whose local state space has elements, this approach yields unified treatment the well-known additive cancellative dualities. spaces three or more we discover several new

We consider K-semialgebras for a commutative semiring K that are at the same time Σ-algebras and satisfy certain linearity conditions. When each finite system of guarded polynomial fixed point equations has a unique solution over such an algebra, then we call it an iterative multi-linear K-Σ-semialgebra. Examples of such algebras include the algebras of Σ-tree series over an alphabet A with coe...