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Conway and iteration hemirings [article]

M. Droste, Z. Esik, W. Kuich
2013 arXiv   pre-print
We provide an analysis of the relationship between 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.  ... 
arXiv:1307.0725v2 fatcat:lrw2gz25lrd4pplmesbah3ikqu

Free iterative and iteration K-semialgebras [article]

Zoltan Esik, Werner Kuich
2011 arXiv   pre-print
We consider algebras of rational power series over an alphabet Σ with coefficients in a commutative 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 ∞ |.  ... 
arXiv:1008.1507v2 fatcat:tkeubk5iqna2fno5io2a7ly5l4

An Algebraic Approach to Energy Problems I — *-Continuous Kleene ω-Algebras

Zoltán Ésik, Uli Fahrenberg, Axel Legay, Karin Quaas
2017 Acta Cybernetica  
We also show that every * -continuous Kleene ω-algebra gives rise to an 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  ... 
doi:10.14232/actacyb.23.1.2017.13 fatcat:tefpfb24m5d43jsmrtclcpwcee

*-Continuous Kleene $$\omega $$ ω -Algebras [chapter]

Zoltán Ésik, Uli Fahrenberg, Axel Legay
2015 Lecture Notes in Computer Science  
We show that * -continuous Kleene ω-algebras give rise to 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  ... 
doi:10.1007/978-3-319-21500-6_19 fatcat:5ehzf5pevjdx5fayx2uy3y6o7u

*-Continuous Kleene ω-Algebras [article]

Zoltán Ésik, Uli Fahrenberg
2015 arXiv   pre-print
We show that *-continuous Kleene ω-algebras give rise to 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  ... 
arXiv:1501.01118v1 fatcat:dez4bltmxre3bgtwdgu62mosfi

Kleene Algebras and Semimodules for Energy Problems [chapter]

Zoltán Ésik, Uli Fahrenberg, Axel Legay, Karin Quaas
2013 Lecture Notes in Computer Science  
Uncovering a close connection between energy problems 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] .  ... 
doi:10.1007/978-3-319-02444-8_9 fatcat:uas2zcvd6zhsjmtoyxm3yjdoq4

Kleene Algebras and Semimodules for Energy Problems [article]

Zoltán Ésik, Uli Fahrenberg, Axel Legay, Karin Quaas
2013 arXiv   pre-print
Uncovering a close connection between energy problems 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] .  ... 
arXiv:1307.0635v1 fatcat:yrso5bm3vnfavg3d6rxgppy3sm

An Algebraic Approach to Energy Problems II — The Algebra of Energy Functions

Zoltán Ésik, Uli Fahrenberg, Axel Legay, Karin Quaas
2017 Acta Cybernetica  
Energy 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.  ... 
doi:10.14232/actacyb.23.1.2017.14 fatcat:5m5vr6phhfb4lhpaghgb42nn2e

Embracing divergence: a formalism for when your semiring is simply not complete, with applications in quantum simulation [article]

Gregory Crosswhite
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 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  ... 
arXiv:1208.0659v2 fatcat:utt7ngrsoja3pmnpmxgl2g45wm

Subject index volumes 1–200

1999 Theoretical Computer Science  
unifiable 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  ... 
doi:10.1016/s0304-3975(98)00319-3 fatcat:s22ud3iiqjht7lfbtc3zctk7zm

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.  ... 

Fold maps and positive topological quantum field theories

Dominik Wrazidlo
2017
in plenty of valuable 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.  ... 
doi:10.11588/heidok.00023253 fatcat:ctymywhlhnfz3fsoel7kenad4u

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)

Frederik Armknecht, Helena Handschuh, Tetsu Iwata, Bart, Bernd Bremer, Valerio Mohr, Martin Pascucci, Schulz, Erika Ábrahám, Alberto Avritzer, Anne Remke, William Sanders (+13 others)
2014 unpublished
Ésik I will discuss algebraic structures for the behavior of quantitative systems including Conway and iteration semirings, hemirings, semimodules, etc.  ...  state pair.  ...  Facebook's Tastes, ties and Time project and the release of data in 2008.  ... 
fatcat:iqk466everfcdhf5guvz5ph2ee

A generators and relations derivation of Khovanov homology of 2-strand braid links

Omid Hurson
2018 unpublished
results 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 .  ... 
doi:10.25365/thesis.56502 fatcat:o34canu255a4xeofpmwcxuzdou