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Conway and iteration hemirings
[article]

2013
*
arXiv
*
pre-print

We provide an analysis of the relationship between

arXiv:1307.0725v2
fatcat:lrw2gz25lrd4pplmesbah3ikqu
*Conway*hemirings*and*(*partial*)*Conway**semirings**and*describe several free constructions. ...*Iteration*hemirings are*iteration**semirings*without a multiplicative unit. ... We define*Conway**and**iteration*hemiring-hemimodule*pairs**and*study their relation to (*partial*)*Conway**and**iteration**semiring*-*semimodule**pairs*. ...##
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Free iterative and iteration K-semialgebras
[article]

2011
*
arXiv
*
pre-print

We consider algebras of rational power series over an alphabet Σ with coefficients in a commutative

arXiv:1008.1507v2
fatcat:tkeubk5iqna2fno5io2a7ly5l4
*semiring*K*and*characterize them as the free algebras in various classes of algebraic structures. ... Since |s c | = |t c |, s c*and*t c are equivalent by Lemma 11.4. Since |s 0 | = |t 0 |, s 0*and*t 0 are equivalent by Theorem 8.5. ... Write s = s c +s 0 +∞s ∞*and*t = t c +t 0 +t ∞ as in Lemma 11.9. Since |s| = |t|, it follows that |s c | = |t c |, |s 0 | = |t 0 |*and*|∞s ∞ | = |∞t ∞ |. ...##
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An Algebraic Approach to Energy Problems I — *-Continuous Kleene ω-Algebras

2017
*
Acta Cybernetica
*

We also show that every * -continuous Kleene ω-algebra gives rise to an

doi:10.14232/actacyb.23.1.2017.13
fatcat:tefpfb24m5d43jsmrtclcpwcee
*iteration*semiringsemimodule*pair*. ... These involve a * -continuous Kleene algebra with a * -continuous action on a*semimodule**and*an infinite product operation that is also * -continuous. ... An idempotent*semiring*-*semimodule**pair*(S, V ) is a*Conway**semiring*-*semimodule**pair*if it is equipped with a star operation * : S → S*and*an omega operation ω : S → V such that S is a*Conway**semiring*acting ...##
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*-Continuous Kleene $$\omega $$ ω -Algebras
[chapter]

2015
*
Lecture Notes in Computer Science
*

We show that * -continuous Kleene ω-algebras give rise to

doi:10.1007/978-3-319-21500-6_19
fatcat:5ehzf5pevjdx5fayx2uy3y6o7u
*iteration**semiring*-*semimodule**pairs*. We show how our work can be applied to solve certain energy problems for hybrid systems. ... We define*and*study basic properties of * -continuous Kleene ω-algebras that involve a * -continuous Kleene algebra with a * -continuous action on a*semimodule**and*an infinite product operation that is ... We have seen that every * -continuous Kleene ω-algebra is an*iteration**semiring*-*semimodule**pair*, which permits to compute the behavior of Büchi automata with weights in a * -continuous Kleene ω-algebra ...##
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*-Continuous Kleene ω-Algebras
[article]

2015
*
arXiv
*
pre-print

We show that *-continuous Kleene ω-algebras give rise to

arXiv:1501.01118v1
fatcat:dez4bltmxre3bgtwdgu62mosfi
*iteration**semiring*-*semimodule**pairs*. We show how our work can be applied to solve certain energy problems for hybrid systems. ... We define*and*study basic properties of *-continuous Kleene ω-algebras that involve a *-continuous Kleene algebra with a *-continuous action on a*semimodule**and*an infinite product operation that is also ... We have seen that every * -continuous Kleene ω-algebra is an*iteration**semiring*-*semimodule**pair*, which permits to compute the behavior of Büchi automata with weights in a * -continuous Kleene ω-algebra ...##
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Kleene Algebras and Semimodules for Energy Problems
[chapter]

2013
*
Lecture Notes in Computer Science
*

Uncovering a close connection between energy problems

doi:10.1007/978-3-319-02444-8_9
fatcat:uas2zcvd6zhsjmtoyxm3yjdoq4
*and*reachability*and*Büchi acceptance for*semiring*-weighted automata, we show that these generalized energy problems are decidable. ... We also expose a structure of*Conway**semiring*-*semimodule**pair*over energy functions which permits to characterize Büchi acceptance. ... This is a standard result for complete*semiring*-*semimodule**pairs*, cf. [19] . ...##
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Kleene Algebras and Semimodules for Energy Problems
[article]

2013
*
arXiv
*
pre-print

Uncovering a close connection between energy problems

arXiv:1307.0635v1
fatcat:yrso5bm3vnfavg3d6rxgppy3sm
*and*reachability*and*B\"uchi acceptance for*semiring*-weighted automata, we show that these generalized energy problems are decidable. ... We also expose a structure of*Conway**semiring*-*semimodule**pair*over energy functions which permits to characterize Büchi acceptance. ... This is a standard result for complete*semiring*-*semimodule**pairs*, cf. [19] . ...##
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An Algebraic Approach to Energy Problems II — The Algebra of Energy Functions

2017
*
Acta Cybernetica
*

Energy

doi:10.14232/actacyb.23.1.2017.14
fatcat:5m5vr6phhfb4lhpaghgb42nn2e
*and*resource management problems are important in areas such as embedded systems or autonomous systems. ... We recall the energy automata introduced in [28]*and*the decision problems we are interested in. ... FinAdd L,L ) is a*semiring*-*semimodule**pair*. ...##
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Embracing divergence: a formalism for when your semiring is simply not complete, with applications in quantum simulation
[article]

2012
*
arXiv
*
pre-print

In this paper we introduce a new kind of automaton which we call a diverging automaton that maps infinite words to sequences of weights from a

arXiv:1208.0659v2
fatcat:utt7ngrsoja3pmnpmxgl2g45wm
*semiring**and*which employs a Buchi-like boundary condition ... Specifically, rather than taking coefficients from an arbitrary*semiring*S we instead take them from S^N. ... First, it would be good to find a theory that generalizes*and*unites the theory we have just presented here with the theory of*Conway** -*semiring*-ω -*semimodule**pairs*, just as the latter provided a generalization ...##
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Subject index volumes 1–200

1999
*
Theoretical Computer Science
*

unifiable

doi:10.1016/s0304-3975(98)00319-3
fatcat:s22ud3iiqjht7lfbtc3zctk7zm
*pairs*, , 1516 Cazanescu*and*-, 806 unifiable*pairs*, , 1598 Cazanescu*and*-, 806 unifiable*pairs*, , 1604 Cazanescu*and*-, 806 unifiable*pairs*, , 1620 Cazanescu*and*-, 806 unifiable*pairs*, . 1796 ...*pairs*, ,2159 Cazanescu*and*-, 806 unifiable*pairs*, , 2175 Cazanescu*and*-, 806 unifiable*pairs*, ,2200 Cazanescu*and*-, 806 unifiable*pairs*, ,2276 Cazanescu*and*-, 806 unifiable*pairs*, ,22Y5,2336 Cazanescu ...##
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Page 297 of Mathematical Reviews Vol. , Issue Index
[page]

*
Mathematical Reviews
*

Spectra of endomorphisms of

*semimodules*over*semirings*with an idempotent operation. (Russian) Dokl. Akad. Nauk SSSR 308 (1989), no. 4, 780-783; translation in Soviet Math. ... [*Pairs*of functions*and*false billiards] Topology 28 (1989), no. 4, 439-452. (Henk Broer) 91d:58177 58F14 (58C27, 58F10, 58F21) — Linéarisation de certaines structures de Poisson. ...##
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Fold maps and positive topological quantum field theories

2017

in plenty of valuable

doi:10.11588/heidok.00023253
fatcat:ctymywhlhnfz3fsoel7kenad4u
*and*insightful conversations. ... By virtue of a general framework that is based on the concept of Eilenberg completeness of*semirings*from computer science, a positive TFT can be produced rigorously via quantization of systems of fields ... The concept of a complete*semiring*goes back to Eilenberg [12]*and*incorporates ideas due to*Conway*from automata theory*and*formal languages. ...##
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Connecting Performance Analysis and Visualization to Advance Extreme Scale Computing (Dagstuhl Seminar 14022) Randomized Timed and Hybrid Models for Critical Infrastructures (Dagstuhl Seminar 14031) Planning with Epistemic Goals (Dagstuhl Seminar 14032)

2014
unpublished

Ésik I will discuss algebraic structures for the behavior of quantitative systems including

fatcat:iqk466everfcdhf5guvz5ph2ee
*Conway**and**iteration**semirings*, hemirings,*semimodules*, etc. ... state*pair*. ... Facebook's Tastes, ties*and*Time project*and*the release of data in 2008. ...##
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A generators and relations derivation of Khovanov homology of 2-strand braid links

2018
unpublished

results

doi:10.25365/thesis.56502
fatcat:o34canu255a4xeofpmwcxuzdou
*and*conjectural predictions by Anokhina-Morozov, Carqueville-Murfet, Dolotin-Morozov, Gukov-Iqbal-Kozcaz-Vafa,*and*Rasmussen. ... By using this technique, we are able to provide a computation of the level n Khovanov-Rozansky invariant of the 2-strand braid link with k crossings, for arbitrary n*and*k, confirming*and*extending previous ... This makes pFC MOY ,`q a*semimodule*for the*semiring*Z ě0 rq, q´1s. Notice that the Z ě0 rq, q´1s-action preserves both the source*and*the target sequences of elements in FC MOY . ...