An approach to schedule development in project management is proposed based on models and methods of idempotent algebra. The approach offers a way to represent various types of precedence relationships among activities in projects as linear vector equations in terms of an idempotent semiring. As a result, many issues in project scheduling reduce to solving computational problems in the idempote...

On the space of nondepraved (see [8]) real, isolated singularities, we consider the stable equivalence relation induced by smooth deformations whose asymptotic behaviour is controlled by the Palais-Smale condition. It is shown that the resulting space of equivalence classes admits a canonical semiring structure and is isomorphic to the semiring of stable homotopy classes of CW-complexes. In an ...

We show that finite λ-bisimulations (closely related to bisimulations up to context) are sound and complete for finitely generated λ-bialgebras for distributive laws λ of a monad T on Set over an endofunctor F on Set, such that F preserves weak pullbacks and finitely generated T -algebras are closed under taking kernel pairs. This result is used to infer the decidability of weighted language eq...

The paper presents Entropy Semiring Forwardbackward algorithm (ESRFB) and its application for memory efficient computation of the subsequence constrained entropy and state sequence entropy of a Hidden Markov Model (HMM) when an observation sequence is given. ESRFB is based on forwardbackward recursion over the entropy semiring, having the lower memory requirement than the algorithm developed by...

The aim of the paper is to show an example of interaction between the AI and OR elds of research using the Constraint Programming (CP) framework to glue them together. We solve a shortest path problem using the c-semiring-based framework for programming over soft constraints (SCLP), which is an extension of classical constraint solving and programming. The SCLP approac handle uniformly several ...

Simulations of weighted tree automata (wta) are considered. It is shown how such simulations can be decomposed into simpler functional and dual functional simulations also called forward and backward simulations. In addition, it is shown in several cases (fields, commutative rings, Noetherian semirings, semiring of natural numbers) that all equivalent wta M and N can be joined by a finite chain...

We give a lower bound on the speed at which Newton’s method (as defined in [5, 6]) converges over arbitrary ω-continuous commutative semirings. From this result, we deduce that Newton’s method converges within a finite number of iterations over any semiring which is “collapsed at some k ∈ N” (i.e. k = k + 1 holds) in the sense of [1]. We apply these results to (1) obtain a generalization of Par...