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1
Content available remote A variant of Jensen’s functional equation on semigroups
EN
We determine the solutions f : S → H of the following functional equation f(xy) + f(σ(y)x) = 2f(x), x,y∈S, and the solutions f1, f2, f3 : M → H of the functional equation f1(xy) + f2(σ(y)x) = 2f3(x), x,y∈M, where S is a semigroup, M is a monoid, H is an abelian group 2-torsion free, and σ is an involutive automorphism.
EN
The Sardinas-Patterson's test for codes has contributed many effective testing algorithms to the development of theory of codes, formal languages, etc. However, we will show that a modification of this test proposed in this paper can deduce more effective testing algorithms for codes. As a consequence, we establish a quadratic algorithm that, given as input a regular language X defined by a tuple (ϕ, M, B), where ϕ : A* → M is a monoid morphism saturating X, M is a finite monoid, B Í M, X = ϕ−1(B), decides in time complexity O(n2) whether X is a code, where n = Card(M). Specially, n can be chosen as the finite index of X. A quadratic algorithm for testing of ◊-codes is also established.
EN
We give a new proof of the Krohn-Rhodes theorem using local divisors. The proof provides nearly as good a decomposition in terms of size as the holonomy decomposition of Eilenberg, avoids induction on the size of the state set, and works exclusively with monoids with the base case of the induction being that of a group.
4
Content available remote Towards a Framework for Modelling Behaviours of Hybrid Systems
EN
The paper is devoted to characterizing hybrid systems by specifying their possible runs, called processes, where each process is represented by a pomset in an intrinsic, global time independent way and can possibly be obtained by composing seąuentially and in parallel other processes.
PL
Praca dotyczy opisywania systemów hybrydowych poprzez definiowanie przebiegów ich działania zwanych procesami, gdzie procesy są reprezentowane strukturami częściowo uporządkowanymi i mog^ być definiowane przez szeregowe i równoległe składanie wcześniej zdefiniowanych procesów.
EN
We investigate the problem of finding monoids that recognize languages of the form L1\JoinTL2 where T is an arbitrary set of routes. We present a uniform method based on routes to find such monoids. Many classical operations from the theory of formal languages, such as catenation, bi-catenation, simple splicing, shuffle, literal shuffle, and insertion are shown to be just particular instances of the operation T.
7
Content available remote Note on logics of idempontents
EN
The main result of this paper is the characterization of certain logics of idempotents by Boolean semirings. Moreover some interesting examples are likewise added.
EN
In [9] submonoids of a commutative monoid are characterized by means of their relations of domination, subgroups of a commutative monoid are characterized by means of their relations of double domination. The main purpose of this paper is to transfer these results to general monoids. The important means will be certain relations, which we shall study in detail.
EN
Prelanguages and pregrammars introduced present a generalization of languages and pure grammars. Relation of domination and double domination may be easily transferred from languages to prelanguages. In the present paper submonoids of a commutative monoid are characterized by means of their relations of domination: subgroups of a commutative group are characterized by means of their relations of double domination. The submonoid generated by a subset of a commutative monoid is constructed using a suitable pregrammar.
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