A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Kleene Algebra with Observations
[article]

2019
*
arXiv
*
pre-print

In this paper, we propose

arXiv:1811.10401v3
fatcat:3tbaptzye5gvjel3cbqhc5khni
*Kleene**algebra**with**observations*(KAO), a variant of KAT, as an alternative foundation for extending KAT to a concurrent setting. ...*Kleene**algebra**with*tests (KAT) is an*algebraic*framework for reasoning about the control flow of sequential programs. ... We call this system weak*Kleene**algebra**with**observations*; like KAT, its axioms are based on the axioms of Boolean*algebra*and*Kleene**algebra*, as follows. Definition 4.1 (WKAO axioms). ...##
###
Concurrent Kleene Algebra with Observations: From Hypotheses to Completeness
[chapter]

2020
*
Lecture Notes in Computer Science
*

It turns out that integrating tests in CKA is subtle, due to their interaction

doi:10.1007/978-3-030-45231-5_20
fatcat:hiblehptwnh2hboxqvqyctx5qi
*with*parallelism. In this paper we provide a solution in the form of Concurrent*Kleene**Algebra**with**Observations*(CKAO). ... Concurrent*Kleene**Algebra*(CKA) extends basic*Kleene**algebra**with*a parallel composition operator, which enables reasoning about concurrent programs. ...*Algebra**with**Observations*(KAO) in previous work [13] . ...##
###
Concurrent Kleene Algebra with Observations: from Hypotheses to Completeness
[article]

2020
*
arXiv
*
pre-print

It turns out that integrating tests in CKA is subtle, due to their interaction

arXiv:2002.09682v1
fatcat:uv4z53k755hd7kiubof4ijoazi
*with*parallelism. In this paper we provide a solution in the form of Concurrent*Kleene**Algebra**with**Observations*(CKAO). ... Concurrent*Kleene**Algebra*(CKA) extends basic*Kleene**algebra**with*a parallel composition operator, which enables reasoning about concurrent programs. ... In order to fix this issue, we have presented*Kleene**Algebra**with**Observations*(KAO) in previous work [13] . ...##
###
Kleene Algebras and Logic: Boolean and Rough Set Representations, 3-valued, Rough and Perp Semantics
[article]

2015
*
arXiv
*
pre-print

One concludes

arXiv:1511.07165v1
fatcat:kyjzxlniqjc2rimgy35cmpm5uq
*with*the*observation*that all the semantics for this logic are equivalent. ... A structural theorem for*Kleene**algebras*is proved, showing that an element of a*Kleene**algebra*can be looked upon as an ordered pair of sets. ... Let us spell out the natural connections of the*Kleene**algebra*3*with*rough sets. ...##
###
A Free Construction of Kleene Algebras with Tests
[chapter]

2004
*
Lecture Notes in Computer Science
*

Moreover we show that our free

doi:10.1007/978-3-540-27764-4_8
fatcat:u426j6wuzze4devtfy6gpg2iue
*Kleene**algebra**with*tests is isomorphic to Kozen and Smith's*Kleene**algebra**with*tests if their construction available, that is, a generator of the Boolean*algebra*is finite ... In this paper we define*Kleene**algebra**with*tests in a slightly more general way than Kozen's definition. ... Due to this*observation*, we define a*Kleene**algebra**with*tests as a triple consisting of a Boolean*algebra*, a*Kleene**algebra*, and a function from the carrier set of the Boolean*algebra*to the carrier of ...##
###
A Completeness Theorem for Kleene Algebras and the Algebra of Regular Events

1994
*
Information and Computation
*

Unlike Salomaa's axiomatizations, the axiomatization given here is sound for all interpretations over

doi:10.1006/inco.1994.1037
fatcat:qjketrvu25bunju4xlvfobmkse
*Kleene**algebras*. ... We give a nitary axiomatization of the*algebra*of regular events involving only equations and equational implications. ... Introduction*Kleene**algebras*are*algebraic*structures*with*operators +, , , 0, and 1 satisfying certain axioms. ...##
###
Prime filter structures of pseudocomplemented Kleene algebras and representation by rough sets
[article]

2019
*
arXiv
*
pre-print

We introduce

arXiv:1806.09203v3
fatcat:ltetwjitgfhsdoay4k74l6b4by
*Kleene*-Varlet spaces as partially ordered sets equipped*with*a polarity satisfying certain additional conditions. ... By applying*Kleene*-Varlet spaces, we prove that each regular pseudocomplemented*Kleene**algebra*is isomorphic to a subalgebra of the rough set regular pseudocomplemented*Kleene**algebra*defined by a tolerance ... Let (X, ≤, g) be a*Kleene*-Varlet space. Here we present some*observations*related to the map g. ...##
###
MV-algebras freely generated by finite Kleene algebras

2013
*
Algebra Universalis
*

variety of MV-

doi:10.1007/s00012-013-0250-3
fatcat:royq43fn4rgr5cawihe6g4543u
*algebras*, W is the variety of*Kleene**algebras*, and B is finitely generated--equivalently, finite. ... The proofs rely heavily on the Davey-Werner natural duality for*Kleene**algebras*, on the representation of finitely presented MV-*algebras*by compact rational polyhedra, and on the theory of bases of MV-*algebras*... (III) If A is an MV-*algebra**with*a basis B, the multipliers of B are uniquely determined [17, (iii ) (*Observe*that ∅ ∈ B whenever 0 = 1 in A, i.e., whenever A is non-trivial. ...##
###
Modal Tools for Separation and Refinement

2008
*
Electronical Notes in Theoretical Computer Science
*

*Kleene*modules and modal

*Kleene*

*algebras*are applied to automatically verify refinement laws for infinite loops and separation of termination. ... defined, and

*with*∅ and P as neutral elements is a

*Kleene*

*algebra*. ... So a

*Kleene*

*algebra*

*with*(Boolean) domain is simply a (Boolean) domain semiring that is also a

*Kleene*

*algebra*. ...

##
###
Relation-Algebraic Verification of Prim's Minimum Spanning Tree Algorithm
[chapter]

2016
*
Lecture Notes in Computer Science
*

Many existing results from relation

doi:10.1007/978-3-319-46750-4_4
fatcat:7mcpqvvxgzerzfbyenz7usw4lu
*algebras*and*Kleene**algebras*generalise from the relation model to the weighted-graph model*with*no or small changes. ... We introduce new generalisations of relation*algebras*and*Kleene**algebras*, in which most of the proof can be carried out. ... I thank Peter Höfner and Bernhard Möller for discussing alternative approaches to minimum spanning trees in*Kleene**algebras*. ...##
###
Kleene algebras, adjunction and structural control
[article]

2018
*
arXiv
*
pre-print

In the present paper, we introduce a multi-type calculus for the logic of measurable

arXiv:1805.07583v1
fatcat:egfclzr43zgx5h276ueeah4bti
*Kleene**algebras*, for which we prove soundness, completeness, conservativity, cut elimination and subformula property ... In this paper, we introduce a subclass of*Kleene**algebras*, referred to as measurable*Kleene**algebras*, 2 which are*Kleene**algebras*endowed*with*a dual*Kleene*star operation, associating any element*with*... Next, we introduce a subclass of*Kleene**algebras*endowed*with*both a*Kleene*star and a dual*Kleene*star. ...##
###
Kleene algebra with tests

1997
*
ACM Transactions on Programming Languages and Systems
*

We introduce

doi:10.1145/256167.256195
fatcat:asxkldtklfefjnfjzgyjl4j36e
*Kleene**algebra**with*tests, an equational system for manipulating programs. ... The proof illustrates the use of*Kleene**algebra**with*tests and commutativity conditions in program equivalence proofs. ... In Section 4.1, we*observe*that the universal Horn theory of the *-continuous*Kleene**algebras*is not recursively enumerable, therefore not finitely axiomatizable. ...##
###
Kleene posets and pseudo-Kleene posets
[article]

2020
*
arXiv
*
pre-print

The concept of a

arXiv:2006.04417v1
fatcat:pj6s2wazmffennhih5j2te4pma
*Kleene**algebra*(sometimes also called*Kleene*lattice) was already generalized by the first author for non-distributive lattices under the name pseudo-*Kleene**algebra*. ... Moreover, we prove that the Dedekind-MacNeille completion of a pseudo-*Kleene*poset is a pseudo-*Kleene**algebra*and that the Dedekind-MacNeille completion of a finite*Kleene*poset is a*Kleene**algebra*. ... A*Kleene**algebra*(see [10] ) is a distributive pseudo-*Kleene**algebra*.*Observe*that a lattice*with*an antitone involution is a (pseudo-)*Kleene*poset if and only if it is a (pseudo-)*Kleene**algebra*. ...##
###
Kleene algebras are almost universal

1986
*
Bulletin of the Australian Mathematical Society
*

This paper concerns endomorphism monoids of

doi:10.1017/s0004972700010248
fatcat:xvthmjj3xjcynaojoe5fsr43zy
*Kleene**algebras*and complements [31, which deals*with*endomorphism monoids of de Morgan*algebras*. ...*Kleene**algebras*form a subvariety of de Morgan*algebras*containing Boolean*algebras*. ... We have already*observed*in Section 2 that the number of non-constant endomorphisms of a finite*Kleene**algebra*increases*with*the size of the*algebra*. ...##
###
Design Methodology for the Implementation of Fuzzy Inference Systems Based on Boolean Relations

2019
*
Electronics
*

The methodology uses

doi:10.3390/electronics8111243
fatcat:q5jut64i3rfvdogh4agjmhprjq
*Kleene**algebra*via truth tables for the fuzzy system design, allowing the simplification of the equations that implement the fuzzy system. ... In comparison*with*the Boolean*algebra*in*Kleen**algebra*is*observable*that: x ∨ x ≤ 1 (7) x ∧ x ≥ 0 For the FIS-BBR design process proposed, the distributive and absorption properties are especially used ... , being an important aspect the manipulation done*with*Boolean and*Kleene**algebras*. ...
« Previous

*Showing results 1 — 15 out of 4,150 results*