Paul, Erik Equivalence, unambiguity, and sequentiality of finitely ambiguous max-plus tree automata. (English) Zbl 07805936 Int. J. Found. Comput. Sci. 35, No. 1-2, 23-49 (2024). MSC: 68Qxx 68-XX 90Cxx PDFBibTeX XMLCite \textit{E. Paul}, Int. J. Found. Comput. Sci. 35, No. 1--2, 23--49 (2024; Zbl 07805936) Full Text: DOI
Izhakian, Zur; Merlet, Glenn Tropical linear representations of the Chinese monoid. (English) Zbl 1522.20216 Semigroup Forum 107, No. 1, 144-157 (2023). Reviewer: Thodsaporn Kumduang (Nakhon Pathom) MSC: 20M05 05E10 16Y60 20M07 PDFBibTeX XMLCite \textit{Z. Izhakian} and \textit{G. Merlet}, Semigroup Forum 107, No. 1, 144--157 (2023; Zbl 1522.20216) Full Text: DOI arXiv
Almagor, Shaull; Boker, Udi; Kupferman, Orna What’s decidable about weighted automata? (English) Zbl 1526.68003 Inf. Comput. 282, Article ID 104651, 20 p. (2022). MSC: 68Q45 PDFBibTeX XMLCite \textit{S. Almagor} et al., Inf. Comput. 282, Article ID 104651, 20 p. (2022; Zbl 1526.68003) Full Text: DOI Link
Stier, Kevin; Ulbricht, Markus Disambiguation of weighted tree automata. (English) Zbl 07614750 Han, Yo-Sub (ed.) et al., Descriptional complexity of formal systems. 23rd IFIP WG 1.02 international conference, DCFS 2021, virtual event, September 5, 2021. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 13037, 163-175 (2021). MSC: 68Qxx PDFBibTeX XMLCite \textit{K. Stier} and \textit{M. Ulbricht}, Lect. Notes Comput. Sci. 13037, 163--175 (2021; Zbl 07614750) Full Text: DOI
Colcombet, Thomas The factorisation forest theorem. (English) Zbl 07469516 Pin, Jean-Éric (ed.), Handbook of automata theory. Volume I. Theoretical foundations. Berlin: European Mathematical Society (EMS). 653-693 (2021). MSC: 68Q70 03D05 20M35 PDFBibTeX XMLCite \textit{T. Colcombet}, in: Handbook of automata theory. Volume I. Theoretical foundations. Berlin: European Mathematical Society (EMS). 653--693 (2021; Zbl 07469516) Full Text: DOI
Lombardy, Sylvain; Mairesse, Jean Max-plus automata. (English) Zbl 1510.68039 Pin, Jean-Éric (ed.), Handbook of automata theory. Volume I. Theoretical foundations. Berlin: European Mathematical Society (EMS). 151-188 (2021). MSC: 68Q45 15A80 16Y60 68Q70 PDFBibTeX XMLCite \textit{S. Lombardy} and \textit{J. Mairesse}, in: Handbook of automata theory. Volume I. Theoretical foundations. Berlin: European Mathematical Society (EMS). 151--188 (2021; Zbl 1510.68039) Full Text: DOI
Paul, Erik Finite sequentiality of unambiguous max-plus tree automata. (English) Zbl 1517.68211 Theory Comput. Syst. 65, No. 4, 736-776 (2021). MSC: 68Q45 PDFBibTeX XMLCite \textit{E. Paul}, Theory Comput. Syst. 65, No. 4, 736--776 (2021; Zbl 1517.68211) Full Text: DOI
Maslov, V. P. Submathematics and tropical mathematics. (English) Zbl 1468.00005 Math. Notes 109, No. 2, 241-246 (2021). MSC: 00A30 01A80 14Txx 15A80 PDFBibTeX XMLCite \textit{V. P. Maslov}, Math. Notes 109, No. 2, 241--246 (2021; Zbl 1468.00005) Full Text: DOI
Alqahtani, Mesfer; Özel, Cenap; Zekraoui, Hanifa; Alshammari, Ibtesam Systems of \(\omega \)-linear balances over symmetrized omega algebra. (English) Zbl 1499.16137 JP J. Algebra Number Theory Appl. 47, No. 2, 181-215 (2020). MSC: 16Y60 16Y99 PDFBibTeX XMLCite \textit{M. Alqahtani} et al., JP J. Algebra Number Theory Appl. 47, No. 2, 181--215 (2020; Zbl 1499.16137) Full Text: DOI
Alqahtani, Mesfer; Özel, Cenap; Zekraoui, Hanifa Construction of some symmetrized omega algebras. (English) Zbl 1499.15090 JP J. Algebra Number Theory Appl. 47, No. 2, 157-180 (2020). MSC: 15A80 16Y60 54F15 PDFBibTeX XMLCite \textit{M. Alqahtani} et al., JP J. Algebra Number Theory Appl. 47, No. 2, 157--180 (2020; Zbl 1499.15090) Full Text: DOI
Quintero, Karla; Aguilar, Jose; Niel, Eric; Pietrac, Laurent Towards a tropical automaton product minimizing global completion times. (English) Zbl 1463.90076 Comput. Appl. Math. 39, No. 3, Paper No. 221, 27 p. (2020). MSC: 90B35 68Q45 PDFBibTeX XMLCite \textit{K. Quintero} et al., Comput. Appl. Math. 39, No. 3, Paper No. 221, 27 p. (2020; Zbl 1463.90076) Full Text: DOI
Morrison, Ralph Tropical geometry. (English) Zbl 1441.14208 Harris, Pamela E. (ed.) et al., A project-based guide to undergraduate research in mathematics. Starting and sustaining accessible undergraduate research. Cham: Birkhäuser. Found. Undergrad. Res. Math., 63-105 (2020). MSC: 14Txx 14-01 PDFBibTeX XMLCite \textit{R. Morrison}, in: A project-based guide to undergraduate research in mathematics. Starting and sustaining accessible undergraduate research. Cham: Birkhäuser. 63--105 (2020; Zbl 1441.14208) Full Text: DOI arXiv
Paul, Erik Finite sequentiality of unambiguous max-plus tree automata. (English) Zbl 1517.68212 Niedermeier, Rolf (ed.) et al., 36th international symposium on theoretical aspects of computer science, STACS 2019, March 13–16, 2019, Berlin, Germany. Wadern: Schloss Dagstuhl – Leibniz Zentrum für Informatik. LIPIcs – Leibniz Int. Proc. Inform. 126, Article 55, 17 p. (2019). MSC: 68Q45 PDFBibTeX XMLCite \textit{E. Paul}, LIPIcs -- Leibniz Int. Proc. Inform. 126, Article 55, 17 p. (2019; Zbl 1517.68212) Full Text: DOI
Pin, Jean-Éric Tribute: The influence of Imre Simon’s work in the theory of automata, languages and semigroups. (English) Zbl 1409.01057 Semigroup Forum 98, No. 1, 1-8 (2019). MSC: 01A70 PDFBibTeX XMLCite \textit{J.-É. Pin}, Semigroup Forum 98, No. 1, 1--8 (2019; Zbl 1409.01057) Full Text: DOI
Joseph, Michael Antichain toggling and rowmotion. (English) Zbl 1409.05218 Electron. J. Comb. 26, No. 1, Research Paper P1.29, 43 p. (2019). MSC: 05E18 06A07 PDFBibTeX XMLCite \textit{M. Joseph}, Electron. J. Comb. 26, No. 1, Research Paper P1.29, 43 p. (2019; Zbl 1409.05218) Full Text: arXiv Link
Hong, Hoon; Sendra, J. Rafael Number of common roots and resultant of two tropical univariate polynomials. (English) Zbl 1402.15019 J. Algebra 511, 420-439 (2018). Reviewer: Hulya Arguz (London) MSC: 15A80 14T05 15A15 12K10 PDFBibTeX XMLCite \textit{H. Hong} and \textit{J. R. Sendra}, J. Algebra 511, 420--439 (2018; Zbl 1402.15019) Full Text: DOI arXiv
Gondim, Rodrigo; Zappalà, Giuseppe Lefschetz properties for Artinian Gorenstein algebras presented by quadrics. (English) Zbl 1409.13002 Proc. Am. Math. Soc. 146, No. 3, 993-1003 (2018). Reviewer: Juan C. Migliore (Notre Dame) MSC: 13A02 05E40 13D40 13E10 PDFBibTeX XMLCite \textit{R. Gondim} and \textit{G. Zappalà}, Proc. Am. Math. Soc. 146, No. 3, 993--1003 (2018; Zbl 1409.13002) Full Text: DOI arXiv
Paul, Erik The equivalence, unambiguity and sequentiality problems of finitely ambiguous max-plus tree automata are decidable. (English) Zbl 1441.68128 Larsen, Kim G. (ed.) et al., 42nd international symposium on mathematical foundations of computer science, MFCS 2017, August 21–25, 2017, Aalborg, Denmark. Wadern: Schloss Dagstuhl – Leibniz Zentrum für Informatik. LIPIcs – Leibniz Int. Proc. Inform. 83, Article 53, 13 p. (2017). MSC: 68Q45 PDFBibTeX XMLCite \textit{E. Paul}, LIPIcs -- Leibniz Int. Proc. Inform. 83, Article 53, 13 p. (2017; Zbl 1441.68128) Full Text: DOI
Davydow, A. New algorithms for solving tropical linear systems. (English. Russian original) Zbl 1377.15015 St. Petersbg. Math. J. 28, No. 6, 727-740 (2017); translation from Algebra Anal. 28, No. 6, 1-19 (2016). MSC: 15A80 14T05 15A06 68Q17 PDFBibTeX XMLCite \textit{A. Davydow}, St. Petersbg. Math. J. 28, No. 6, 727--740 (2017; Zbl 1377.15015); translation from Algebra Anal. 28, No. 6, 1--19 (2016) Full Text: DOI arXiv
Dokuchaev, Mikhailo; Kirichenko, Vladimir; Kudryavtseva, Ganna; Plakhotnyk, Makar The max-plus algebra of exponent matrices of tiled orders. (English) Zbl 1406.16016 J. Algebra 490, 1-20 (2017). MSC: 16H05 16Z99 15A80 16G30 PDFBibTeX XMLCite \textit{M. Dokuchaev} et al., J. Algebra 490, 1--20 (2017; Zbl 1406.16016) Full Text: DOI arXiv
Maslov, V. P.; Maslova, T. V. A generalized number theory problem applied to ideal liquids and to terminological lexis. (English) Zbl 1406.91394 Russ. J. Math. Phys. 24, No. 1, 96-110 (2017). MSC: 91F20 11N80 91F10 82D15 82B26 PDFBibTeX XMLCite \textit{V. P. Maslov} and \textit{T. V. Maslova}, Russ. J. Math. Phys. 24, No. 1, 96--110 (2017; Zbl 1406.91394) Full Text: DOI
Sabel, David; Zantema, Hans Termination of cycle rewriting by transformation and matrix interpretation. (English) Zbl 1398.68281 Log. Methods Comput. Sci. 13, No. 1, Paper No. 11, 38 p. (2017). MSC: 68Q42 PDFBibTeX XMLCite \textit{D. Sabel} and \textit{H. Zantema}, Log. Methods Comput. Sci. 13, No. 1, Paper No. 11, 38 p. (2017; Zbl 1398.68281) Full Text: DOI arXiv
Hong, Hoon; Kim, Yonggu; Scholten, Georgy; Sendra, J. Rafael Resultants over commutative idempotent semirings. I: Algebraic aspect. (English) Zbl 1360.16041 J. Symb. Comput. 79, Part 2, 285-308 (2017). MSC: 16Y60 12K10 13P15 PDFBibTeX XMLCite \textit{H. Hong} et al., J. Symb. Comput. 79, Part 2, 285--308 (2017; Zbl 1360.16041) Full Text: DOI arXiv
Maslov, V. P. Thermodynamics, idempotent analysis, and tropical geometry as a return to primitivism. (English) Zbl 1351.82029 Russ. J. Math. Phys. 23, No. 2, 278-280 (2016). MSC: 82B30 82D30 00A30 PDFBibTeX XMLCite \textit{V. P. Maslov}, Russ. J. Math. Phys. 23, No. 2, 278--280 (2016; Zbl 1351.82029) Full Text: DOI
Izhakian, Zur Semigroup identities of tropical matrix semigroups of maximal rank. (English) Zbl 1377.15016 Semigroup Forum 92, No. 3, 712-732 (2016); erratum ibid. 97, No. 3, 571 (2018). Reviewer: Andreas Arvanitoyeorgos (Patras) MSC: 15A80 15A30 PDFBibTeX XMLCite \textit{Z. Izhakian}, Semigroup Forum 92, No. 3, 712--732 (2016; Zbl 1377.15016) Full Text: DOI
Maslov, V. P. Thermodynamics and tropical mathematics. Definition of quasistatistical processes. (English) Zbl 1342.82057 Russ. J. Math. Phys. 23, No. 1, 101-114 (2016). MSC: 82B30 82D15 PDFBibTeX XMLCite \textit{V. P. Maslov}, Russ. J. Math. Phys. 23, No. 1, 101--114 (2016; Zbl 1342.82057) Full Text: DOI
Maslov, V. P. On tropical analysis. (English) Zbl 1384.14001 Math. Notes 98, No. 5, 798-804 (2015). MSC: 14-03 82-03 82D30 14T05 01A70 01A60 01A61 PDFBibTeX XMLCite \textit{V. P. Maslov}, Math. Notes 98, No. 5, 798--804 (2015; Zbl 1384.14001) Full Text: DOI
Samal, Satya Swarup; Grigoriev, Dima; Fröhlich, Holger; Weber, Andreas; Radulescu, Ovidiu A geometric method for model reduction of biochemical networks with polynomial rate functions. (English) Zbl 1342.92079 Bull. Math. Biol. 77, No. 12, 2180-2211 (2015). MSC: 92C40 92C45 PDFBibTeX XMLCite \textit{S. S. Samal} et al., Bull. Math. Biol. 77, No. 12, 2180--2211 (2015; Zbl 1342.92079) Full Text: DOI arXiv
Litvinov, G. L. Idempotent and tropical mathematics; complexity of algorithms and interval analysis. (English) Zbl 1362.68110 Comput. Math. Appl. 65, No. 10, 1483-1496 (2013). MSC: 68Q25 16Y60 65F99 65G40 68W30 PDFBibTeX XMLCite \textit{G. L. Litvinov}, Comput. Math. Appl. 65, No. 10, 1483--1496 (2013; Zbl 1362.68110) Full Text: DOI arXiv
Torgasin, Svetlana; Zimmermann, Karl-Heinz An all-pairs shortest path algorithm for bipartite graphs. (English) Zbl 1298.05309 Cent. Eur. J. Comput. Sci. 3, No. 4, 149-157 (2013). MSC: 05C85 68Q25 68R10 PDFBibTeX XMLCite \textit{S. Torgasin} and \textit{K.-H. Zimmermann}, Cent. Eur. J. Comput. Sci. 3, No. 4, 149--157 (2013; Zbl 1298.05309) Full Text: DOI
Lu, Xian; Shang, Yun; Lu, Ruqian Automata theory based on lattice-ordered semirings. (English) Zbl 1237.68116 Soft Comput. 15, No. 2, 269-280 (2011). MSC: 68Q45 06F25 PDFBibTeX XMLCite \textit{X. Lu} et al., Soft Comput. 15, No. 2, 269--280 (2011; Zbl 1237.68116) Full Text: DOI
Benedikt, Michael; Puppis, Gabriele; Riveros, Cristian The cost of traveling between languages. (English) Zbl 1333.68304 Aceto, Luca (ed.) et al., Automata, languages and programming. 38th international colloquium, ICALP 2011, Zurich, Switzerland, July 4–8, 2011. Proceedings, Part II. Berlin: Springer (ISBN 978-3-642-22011-1/pbk). Lecture Notes in Computer Science 6756, 234-245 (2011). MSC: 68W32 68Q25 68Q45 PDFBibTeX XMLCite \textit{M. Benedikt} et al., Lect. Notes Comput. Sci. 6756, 234--245 (2011; Zbl 1333.68304) Full Text: DOI
Izhakian, Zur; Margolis, Stuart W. Semigroup identities in the monoid of two-by-two tropical matrices. (English) Zbl 1215.20055 Semigroup Forum 80, No. 2, 191-218 (2010). Reviewer: Zhan Jianming (Enshi) MSC: 20M05 20M20 15A30 16Y60 PDFBibTeX XMLCite \textit{Z. Izhakian} and \textit{S. W. Margolis}, Semigroup Forum 80, No. 2, 191--218 (2010; Zbl 1215.20055) Full Text: DOI arXiv
Kirsten, Daniel A Burnside approach to the termination of Mohri’s algorithm for polynomially ambiguous min-plus-automata. (English) Zbl 1155.68042 Theor. Inform. Appl. 42, No. 3, 553-581 (2008). MSC: 68Q45 68Q70 20M35 PDFBibTeX XMLCite \textit{D. Kirsten}, Theor. Inform. Appl. 42, No. 3, 553--581 (2008; Zbl 1155.68042) Full Text: DOI EuDML Link
Droste, Manfred; Gastin, Paul On aperiodic and star-free formal power series in partially commuting variables. (English) Zbl 1140.68032 Theory Comput. Syst. 42, No. 4, 608-631 (2008). MSC: 68Q45 68Q70 PDFBibTeX XMLCite \textit{M. Droste} and \textit{P. Gastin}, Theory Comput. Syst. 42, No. 4, 608--631 (2008; Zbl 1140.68032) Full Text: DOI
Shang, Yun; Lu, Ruqian Semirings and pseudo MV algebras. (English) Zbl 1124.06006 Soft Comput. 11, No. 9, 847-853 (2007). Reviewer: C. S. Hoo (Edmonton) MSC: 06D35 16Y60 68Q70 PDFBibTeX XMLCite \textit{Y. Shang} and \textit{R. Lu}, Soft Comput. 11, No. 9, 847--853 (2007; Zbl 1124.06006) Full Text: DOI
Lombardy, Sylvain; Mairesse, Jean Series which are both max-plus and min-plus rational are unambiguous. (English) Zbl 1085.68081 Theor. Inform. Appl. 40, No. 1, 1-14 (2006). MSC: 68Q45 68Q70 68Q19 PDFBibTeX XMLCite \textit{S. Lombardy} and \textit{J. Mairesse}, Theor. Inform. Appl. 40, No. 1, 1--14 (2006; Zbl 1085.68081) Full Text: DOI arXiv Numdam EuDML
Kirsten, Daniel Distance desert automata and the star height problem. (English) Zbl 1082.20041 Theor. Inform. Appl. 39, No. 3, 455-509 (2005). Reviewer: Francine Blanchet-Sadri (Greensboro) MSC: 20M35 68Q17 68Q70 20M05 PDFBibTeX XMLCite \textit{D. Kirsten}, Theor. Inform. Appl. 39, No. 3, 455--509 (2005; Zbl 1082.20041) Full Text: DOI Numdam EuDML Link
Kobayashi, Nami Some properties of recognizable \(\mathcal Z\)-subsets. (English) Zbl 1026.68080 Theor. Comput. Sci. 293, No. 1, 83-113 (2003). MSC: 68Q45 PDFBibTeX XMLCite \textit{N. Kobayashi}, Theor. Comput. Sci. 293, No. 1, 83--113 (2003; Zbl 1026.68080) Full Text: DOI
d’Alessandro, Flavio; Sakarovitch, Jacques The finite power property in free groups. (English) Zbl 1025.68049 Theor. Comput. Sci. 293, No. 1, 55-82 (2003). MSC: 68Q45 PDFBibTeX XMLCite \textit{F. d'Alessandro} and \textit{J. Sakarovitch}, Theor. Comput. Sci. 293, No. 1, 55--82 (2003; Zbl 1025.68049) Full Text: DOI
Kobayashi, Nami The closure under division and a characterization of the recognizable \({\mathcal Z}\)-subsets. (English) Zbl 0860.68073 RAIRO, Inform. Théor. Appl. 30, No. 3, 209-230 (1996). MSC: 68Q70 PDFBibTeX XMLCite \textit{N. Kobayashi}, RAIRO, Inform. Théor. Appl. 30, No. 3, 209--230 (1996; Zbl 0860.68073) Full Text: DOI EuDML
Gaubert, S. On the Burnside problem for semigroups of matrices in the \((\max,+)\) algebra. (English) Zbl 0858.20050 Semigroup Forum 52, No. 3, 271-292 (1996). Reviewer: U.Hebisch (Freiberg) MSC: 20M05 16Y60 20M20 15B52 20M10 PDFBibTeX XMLCite \textit{S. Gaubert}, Semigroup Forum 52, No. 3, 271--292 (1996; Zbl 0858.20050) Full Text: DOI EuDML
Simon, Imre On semigroups of matrices over the tropical semiring. (English) Zbl 0888.68086 RAIRO, Inform. Théor. Appl. 28, No. 3-4, 277-294 (1994). MSC: 68Q45 68R05 PDFBibTeX XMLCite \textit{I. Simon}, RAIRO, Inform. Théor. Appl. 28, No. 3--4, 277--294 (1994; Zbl 0888.68086) Full Text: DOI EuDML
Simon, Imre The product of rational languages. (English) Zbl 1422.68160 Lingas, Andrzej (ed.) et al., Automata, languages and programming. 20th international colloquium, ICALP 93, Lund, Sweden, July 5–9, 1993. Proceedings. Berlin: Springer-Verlag. Lect. Notes Comput. Sci. 700, 430-444 (1993). MSC: 68Q45 68Q70 68-02 PDFBibTeX XMLCite \textit{I. Simon}, Lect. Notes Comput. Sci. 700, 430--444 (1993; Zbl 1422.68160) Full Text: DOI
Weber, Andreas Distance automata having large finite distance or finite ambiguity. (English) Zbl 0771.68088 Math. Syst. Theory 26, No. 2, 169-185 (1993). MSC: 68Q45 68Q25 PDFBibTeX XMLCite \textit{A. Weber}, Math. Syst. Theory 26, No. 2, 169--185 (1993; Zbl 0771.68088) Full Text: DOI
Leung, Hing On finite automata with limited nondeterminism (extended abstract). (English) Zbl 1493.68194 Havel, Ivan M. (ed.) et al., Mathematical foundations of computer science 1992. 17th international symposium, Prague, Czechoslovakia, August 24–28, 1992. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 629, 355-363 (1992). MSC: 68Q45 PDFBibTeX XMLCite \textit{H. Leung}, Lect. Notes Comput. Sci. 629, 355--363 (1992; Zbl 1493.68194) Full Text: DOI
Krob, Daniel The equality problem for rational series with multiplicities in the tropical semiring is undecidable. (English) Zbl 1425.68213 Kuich, Werner (ed.), Automata, languages and programming. 19th international colloquium, Wien, Austria, July 13–17, 1992. Proceedings. Berlin: Springer-Verlag. Lect. Notes Comput. Sci. 623, 101-112 (1992). MSC: 68Q45 03D05 03D35 16Y60 68Q70 PDFBibTeX XMLCite \textit{D. Krob}, Lect. Notes Comput. Sci. 623, 101--112 (1992; Zbl 1425.68213) Full Text: DOI HAL
Choffrut, Christian Rational relations and rational series. (English) Zbl 0777.68068 Theor. Comput. Sci. 98, No. 1, 5-13 (1992). Reviewer: D.Krob (Paris) MSC: 68Q70 68Q45 16Y60 PDFBibTeX XMLCite \textit{C. Choffrut}, Theor. Comput. Sci. 98, No. 1, 5--13 (1992; Zbl 0777.68068) Full Text: DOI