Deductive Synthesis of Bubble–Sort Using Multisets

Dramnesc, Isabela; Jebelean, Tudor

doi:10.1109/sami48414.2020.9108725

Cited by 6 publications

(7 citation statements)

References 16 publications

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“…It is notable that the set theoretic forms of these laws do not hold i.e. for A ∈ X m , in general, we have: A ∩ A c = 0 and A ∪ A c = m. Counterexamples supporting above statements may be seen by choosing A = {4/a, 2/b, 0/c, 0/d, 3/e} ∈ {a, b, c, d, e} 4 and calculating…”

Section: Notationmentioning

confidence: 99%

“…Index object in Pandas, the Data Science library of Python language, is a multiset. Multisets are also important for analysis of various computer algorithms [3,4,13,16]. Although in mathematics world, one can trace the origins of modern interest in multisets as far as the great mathematician Richard Dedekind (d. 1916), but it is only with the recent advent of Computer Science and allied fields that a renewed interest is being witnessed [5].…”

Section: Introductionmentioning

confidence: 99%

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On the Notion of a Generalized Mapping on Multiset Spaces

Kharal,

Alshehri,

Turki

et al. 2020

Preprint

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A sufficiently generalized concept of mappings on multisets has been introduced, thus resolving a long standing obstacle in structural study of multiset processing. It has been shown that the mapping defined herein can model a vast array of already defined mappings within the domain of Theoretical Computer Science as special cases and also it handels diverse situations in multiset rewriting transformations. Specifically, this paper unifies and generalizes the works of Parikh [18] (1966), Hickman [8] (1980), Khomenko [12] (2003) and Nazmul [17] (2013).

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Section: Notationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the Notion of a Generalized Mapping on Multiset Spaces

Kharal,

Alshehri,

Turki

et al. 2020

Preprint

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“…These algorithms have been synthesized in authors' previous research, see [12,10,7,9]. The tail recursive version of Bubble-Sort that is certified in this paper, was firstly introduced in [8].…”

Section: Related Work Classical Algorithms On Arrays/listsmentioning

confidence: 99%

“…In this paper we focus on the certification of the tail recursive version of the Bubble-Sort algorithm that was firstly introduced in [8]. Initially, the authors applied some special techniques for the automated synthesis from proofs of the algorithm Max-Sort and the corresponding auxiliary functions.…”

Section: Introductionmentioning

confidence: 99%

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Certification of Tail Recursive Bubble--Sort in Theorema and Coq

Dramnesc,

Jebelean,

Stratulat

Kalpa Publications in Computing

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Algorithm certification or program verification have an increasing importance in the current technological landscape, due to the sharp increase in the complexity of software and software using systems and the high potential of adverse effects in case of failure. For instance robots constitute a particular class of systems that can present high risks of such failures. Sorting on the other hand has a growing area of applications, in particular the ones where organizing huge data collections is critical, as for instance in environmental applications.We present an experiment in formal certification of an original version of the Bubble- Sort algorithm that is functional and tail recursive. The certification is performed in parallel both in Theorema and in Coq, this allows to compare the characteristics and the performance of the two systems. In Theorema the proofs are produced automatically in natural style (similar to human proofs), while in Coq they are based on scripts. However, the background theory, the algorithms, and the proof rules in Theorema are composed by the user without any restrictions – thus error prone, while in Coq one can only use the theories and the proof rules that are rigurously checked by the system, and the algorithms are checked for termination.The goal of our experiments is to contribute to a better understanding and estimation of the complexity of such certification tasks and to create a basis for further increase of the level of automation in the two systems and for their possible integration.

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AlCons : Deductive Synthesis of Sorting Algorithms in Theorema

Dramnesc

Jebelean

2021

Lecture Notes in Computer Science

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Deductive Synthesis of Bubble–Sort Using Multisets

Cited by 6 publications

References 16 publications

On the Notion of a Generalized Mapping on Multiset Spaces

On the Notion of a Generalized Mapping on Multiset Spaces

Certification of Tail Recursive Bubble--Sort in Theorema and Coq

AlCons : Deductive Synthesis of Sorting Algorithms in Theorema

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