Hybrid structures applied to modules over semirings

The concept of a hybrid structure in X -semimodules, where X is a semiring, is introduced in this paper. The notions of hybrid subsemimodule and hybrid right (resp., left) ideals are defined and discussed in semirings. We investigate the representations of hybrid subsemimodules and hybrid ideals using hybrid products. We also get some interesting results on t-pure hybrid ideals in X . Furthermore, we show how hybrid products and hybrid intersections are linked. Finally, the characterization theorem is proved in terms of hybrid structures for fully idempotent semirings.

Amalgamation and extensions of summand absorbing modules over a semiring

A submodule [Formula: see text] of [Formula: see text] is summand absorbing, if [Formula: see text] implies [Formula: see text] for any [Formula: see text]. Such submodules often appear in modules over (additively) idempotent semirings, particularly in tropical algebra. This paper studies amalgamation and extensions of these submodules, and more generally of upper bound modules.

THE GREATEST SOLUTION IN THE INEQUALITY OF K X X LX WITH K 2 ISnn;L 2 ISnn;X 2 ISnm ARE A COMPLETE IDEMPOTENT SEMIRINGS OF INTERVAL

The greatest solution of an inequality KX X LX to solve the optimalcontrol problem for P-Temporal Event Graphs, which is to nd the optimal control thatmeets the constraints on the output and constraints imposed on the adjusted model prob-lem (the model matching problem). We give the greatest solution K X X L Xand X H with K; L;X;H matrices whose are entries in a complete idempotent semir-ings. Furthermore, the authors examine the existence of a sucient condition of theprojector in the set of solutions of inequality K X X L X with K; L;X matrixwhose entries are in the complete idempotent semiring. Projectors can be very necessaryto synthesize controllers in manufacturing systems that are constrained by constraintsand some industrial applications. The researcher then examines the requirements forthe presence of the greatest solution was called projector in the set of solutions of theinequality K X X L X with K; L;X matrices whose are entries in an completeidempotent semiring of interval. Researchers describe in more detail the proof of theproperties used to resolve the inequality K X X L X. Before that, we givethe greatest solution of the inequality KX X LX and X G with K; L;X;Gmatrices whose are entries in an complete idempotent semiring of interval

Generation of summand absorbing submodules

An [Formula: see text]-module [Formula: see text] over a semiring [Formula: see text] lacks zero sums (LZS) if [Formula: see text] implies [Formula: see text]. More generally, a submodule [Formula: see text] of [Formula: see text] is “summand absorbing” (SA), if, for all [Formula: see text], [Formula: see text] These relate to tropical algebra and modules over (additively) idempotent semirings, as well as modules over semirings of sums of squares. In previous work, we have explored the lattice of SA submodules of a given LZS module, especially, those that are finitely generated, in terms of the lattice-theoretic Krull dimension. In this paper, we consider which submodules are SA and describe their explicit generation.

Enriching Ontology-based Data Access with Provenance

Ontology-based data access (OBDA) is a popular paradigm for querying heterogeneous data sources by connecting them through mappings to an ontology. In OBDA, it is often difficult to reconstruct why a tuple occurs in the answer of a query. We address this challenge by enriching OBDA with provenance semirings, taking inspiration from database theory. In particular, we investigate the problems of (i) deciding whether a provenance annotated OBDA instance entails a provenance annotated conjunctive query, and (ii) computing a polynomial representing the provenance of a query entailed by a provenance annotated OBDA instance. Differently from pure databases, in our case, these polynomials may be infinite. To regain finiteness, we consider idempotent semirings, and study the complexity in the case of DL-LiteR ontologies. We implement Task (ii) in a state-of-the-art OBDA system and show the practical feasibility of the approach through an extensive evaluation against two popular benchmarks.

Universal algorithms for solving discrete stationary Bellman equations

This paper investigates algorithms for solving discrete stationary (or) matrix Bellman equations over semirings, in particular over tropical and idempotent semirings, Also there are presented some original algorithms, applications and programmed realization.