Monoids of non-halting programs with tests

Panicker, Gayatri; Krishna, K. V.; Bhaduri, Purandar

doi:10.1007/s00012-018-0490-3

Cited by 2 publications

(2 citation statements)

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“…In order to address a problem posed by Jackson and Stokes in [8], present authors introduced the notion of C-sets and studied axiomatization of if-then-else over C-algebras in [15,16]. Every C-algebra has an inbuilt if-then-else action using which we introduce a notion of annihilators in a natural manner, which aid in studying various structural properties of C-algebras.…”

Section: Introductionmentioning

confidence: 99%

On the structure of C-algebras through atomicity and if-then-else

2020

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This paper introduces the notions of atoms and atomicity in Calgebras and obtains a characterisation of atoms in the C-algebra of transformations. Further, this work presents some necessary conditions and sufficient conditions for the atomicity of C-algebras and shows that the class of finite atomic C-algebras is precisely that of finite adas. This paper also uses the if-then-else action to study the structure of C-algebras and classify the elements of the C-algebra of transformations.2010 Mathematics Subject Classification. 08A70, 03G25 and 68N15.

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Section: Introductionmentioning

confidence: 99%

On the structure of C-algebras through atomicity and if-then-else

2020

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“…Panicker et al [12] generalized [11] in the concatenationfree case to allow arbitrary non-halting tests within if-then-else statements, but under sequential evaluation. Recently, they extended this signature by including composition as well, in [13].…”

Section: Introductionmentioning

confidence: 99%

Algebraic properties of `if-then-else` and commutative three-valued tests

Soo

Stokes

2019

Int. J. Algebra Comput.

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This paper establishes a finite axiomatization of possibly non-halting computer programs and tests, with the if-then-else operation. The model is a two-sorted algebra, with one sort being the programs and the other being the tests. The main operation on programs is composition, and 1 and 0 represent the programs skip and loop (i.e. never halts) respectively. Programs are modeled as partial functions on some state space [Formula: see text], with tests modeled as partial predicates on [Formula: see text]. The operations on the tests are the usual logical connectives ∧, ∨, [Formula: see text], [Formula: see text] and [Formula: see text]. In addition, there is the hybrid operation of if-then-else, and the test-valued operation [Formula: see text] on programs which is true when a program halts, and undefined otherwise. The halting operation [Formula: see text] implies that operations of domain [Formula: see text] and domain join ∨ may also be expressed. When tests are assumed to be possibly non-halting, the evaluation strategy of the logical connectives affects the result. Here we model parallel evaluation, as opposed to the common sequential (or short-circuit) evaluation strategy. For example, we view [Formula: see text] as false if either [Formula: see text] or [Formula: see text] is false, even if the other does not halt.

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Monoids of non-halting programs with tests

Cited by 2 publications

References 22 publications

On the structure of C-algebras through atomicity and if-then-else

On the structure of C-algebras through atomicity and if-then-else

Algebraic properties of `if-then-else` and commutative three-valued tests

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Monoids of non-halting programs with tests

Cited by 2 publications

References 22 publications

On the structure of C-algebras through atomicity and if-then-else

On the structure of C-algebras through atomicity and if-then-else

Algebraic properties of if-then-else and commutative three-valued tests

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Algebraic properties of `if-then-else` and commutative three-valued tests