Partial clones

Denecke, Klaus

doi:10.1142/s1793557120501612

Cited by 3 publications

(3 citation statements)

References 13 publications

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“…. , t n )) = n j=1 vb j (s)vb k (t j ), see [7]. Recently, in [1], the concept of the total number of both occurring variables and occurring operation symbols in a term t which is called the length of the term t, and denoted by len(t).…”

Section: T Kumduang and S Leeratanavaleementioning

confidence: 99%

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The partial many-sorted algebras of terms and formulas with fixed variables count

Leeratanavalee,

Kumduang

2023

Discuss. Math. - General Algebra and Applications

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Terms and formulas, which are formal expressions in first and second order languages obtained by alphabets, operation symbols, and relation symbols, are used to study algebras and algebraic systems. In this paper, we introduce the notion of terms with fixed variables count. The partial manysorted superposition operations of such terms and their partial many-sorted algebra satisfying clone axioms as weak identities are presented. We also extend our structures from algebras to algebraic systems via the concept of formulas with fixed variables count. Conditions for the set of such formulas to be closed under taking of superposition of formulas are determined. We construct the partial many-sorted algebra of formulas with fixed variables count and investigate its satisfaction by clone axioms. Finally, we prove that such partial structure is isomorphic to some Menger systems of the same rank of partial multiplace functions.

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Section: T Kumduang and S Leeratanavaleementioning

confidence: 99%

“…For this, the concept of weak identities is given. We recall from [7] that an equation s ≈ t is said to be a weak identity in an algebra A if one side is defined then another side is also defined and both sides are equal. An excellent overview of partial algebras can be found in [3,15].…”

Section: T Kumduang and S Leeratanavaleementioning

confidence: 99%

The partial many-sorted algebras of terms and formulas with fixed variables count

Leeratanavalee,

Kumduang

2023

Discuss. Math. - General Algebra and Applications

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“…The set of all variables that appear in t is denoted by var(t). More background and current trends in the investigation of terms may be found in [5,13,18].…”

Section: Introduction and Basic Propertiesmentioning

confidence: 99%

Algebras of generalized tree languages with fixed variables

Phuapong,

Chansuriya,

Kumduang

2023

ADM

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Tree languages which are sets of terms always play a prominent role in the first-order languages and theoretical computer science. In this paper, tree languages induced by terms with fixed variables are considered. Under the applications of an operation on tree languages, we construct the algebra of such languages having many properties of abstract clones. A strong connection with theory of general functions is given through a representation theorem. Additionally, the semigroup of mappings of which their images are tree languages with fixed variables is given.

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Menger systems of idempotent cyclic and weak near-unanimity multiplace functions

Kumduang

Leeratanavalee

2021

Asian-European J. Math.

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Multiplace functions, which are also called functions of many variables, and their algebras called Menger algebras have been studied in various fields of mathematics. Based on the theory of many-sorted algebras, the primary aim of this paper is to present the ideas of Menger systems and Menger systems of full multiplace functions which are natural generalizations of Menger algebras and Menger algebras of [Formula: see text]-ary operations, respectively. Two specific types of [Formula: see text]-ary operations, which are called idempotent cyclic and weak near-unanimity generated by cyclic and weak near-unanimity terms, are provided. The Menger algebras under consideration have a two-element universe, the elements of which are two specific [Formula: see text]-ary operations. Additionally, we provide necessary and sufficient conditions in which the abstract Menger algebra and the Menger algebras of these two [Formula: see text]-ary operations are isomorphic. An abstract characterization of unitary Menger systems via systems of idempotent cyclic and weak near-unanimity multiplace functions is generally investigated. A strong connection between clone of terms and Menger systems of full multiplace functions is also investigated.

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Partial clones

Cited by 3 publications

References 13 publications

The partial many-sorted algebras of terms and formulas with fixed variables count

The partial many-sorted algebras of terms and formulas with fixed variables count

Algebras of generalized tree languages with fixed variables

Menger systems of idempotent cyclic and weak near-unanimity multiplace functions

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