Skip to main content

2017 | OriginalPaper | Buchkapitel

The Cost of Exactness in Quantitative Reachability

verfasst von : Krishnendu Chatterjee, Laurent Doyen, Thomas A. Henzinger

Erschienen in: Models, Algorithms, Logics and Tools

Verlag: Springer International Publishing

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In the analysis of reactive systems a quantitative objective assigns a real value to every trace of the system. The value decision problem for a quantitative objective requires a trace whose value is at least a given threshold, and the exact value decision problem requires a trace whose value is exactly the threshold. We compare the computational complexity of the value and exact value decision problems for classical quantitative objectives, such as sum, discounted sum, energy, and mean-payoff for two standard models of reactive systems, namely, graphs and graph games.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Andersson, D.: An improved algorithm for discounted payoff games. In: Proceedings of 11th ESSLLI Student Session, pp. 91–98 (2006) Andersson, D.: An improved algorithm for discounted payoff games. In: Proceedings of 11th ESSLLI Student Session, pp. 91–98 (2006)
2.
Zurück zum Zitat Blondin, M., Finkel, A., Göller, S., Haase, C., McKenzie, P.: Reachability in two-dimensional vector addition systems with states is PSPACE-complete. In: Proceedings of LICS: Symposium on Logic in Computer Science, pp. 32–43. IEEE Computer Society (2015) Blondin, M., Finkel, A., Göller, S., Haase, C., McKenzie, P.: Reachability in two-dimensional vector addition systems with states is PSPACE-complete. In: Proceedings of LICS: Symposium on Logic in Computer Science, pp. 32–43. IEEE Computer Society (2015)
3.
Zurück zum Zitat Boker, U., Henzinger, T.A., Otop, J.: The target discounted-sum problem. In: Proceeings of LICS: Symposium on Logic in Computer Science, pp. 750–761. IEEE Computer Society (2015) Boker, U., Henzinger, T.A., Otop, J.: The target discounted-sum problem. In: Proceeings of LICS: Symposium on Logic in Computer Science, pp. 750–761. IEEE Computer Society (2015)
4.
Zurück zum Zitat Bonet, B., Geffner, H.: Solving POMDPs: RTDP-Bel vs. point-based algorithms. In: Proceedings of IJCAI: International Joint Conference on Artificial Intelligence, pp. 1641–1646 (2009) Bonet, B., Geffner, H.: Solving POMDPs: RTDP-Bel vs. point-based algorithms. In: Proceedings of IJCAI: International Joint Conference on Artificial Intelligence, pp. 1641–1646 (2009)
5.
Zurück zum Zitat Bouyer, P., Fahrenberg, U., Larsen, K.G., Markey, N., Srba, J.: Infinite runs in weighted timed automata with energy constraints. In: Cassez, F., Jard, C. (eds.) FORMATS 2008. LNCS, vol. 5215, pp. 33–47. Springer, Heidelberg (2008). doi:10.1007/978-3-540-85778-5_4 CrossRef Bouyer, P., Fahrenberg, U., Larsen, K.G., Markey, N., Srba, J.: Infinite runs in weighted timed automata with energy constraints. In: Cassez, F., Jard, C. (eds.) FORMATS 2008. LNCS, vol. 5215, pp. 33–47. Springer, Heidelberg (2008). doi:10.​1007/​978-3-540-85778-5_​4 CrossRef
6.
Zurück zum Zitat Brázdil, T., Jančar, P., Kučera, A.: Reachability games on extended vector addition systems with states. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol. 6199, pp. 478–489. Springer, Heidelberg (2010). doi:10.1007/978-3-642-14162-1_40 CrossRef Brázdil, T., Jančar, P., Kučera, A.: Reachability games on extended vector addition systems with states. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol. 6199, pp. 478–489. Springer, Heidelberg (2010). doi:10.​1007/​978-3-642-14162-1_​40 CrossRef
7.
Zurück zum Zitat Brihaye, T., Geeraerts, G., Haddad, A., Monmege, B.: To reach or not to reach? efficient algorithms for total-payoff games. In: Proceedings of CONCUR: Concurrency Theory. LIPIcs, vol. 42, pp. 297–310. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2015) Brihaye, T., Geeraerts, G., Haddad, A., Monmege, B.: To reach or not to reach? efficient algorithms for total-payoff games. In: Proceedings of CONCUR: Concurrency Theory. LIPIcs, vol. 42, pp. 297–310. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2015)
8.
Zurück zum Zitat Brim, L., Chaloupka, J., Doyen, L., Gentilini, R., Raskin, J.-F.: Faster algorithms for mean-payoff games. Formal Methods Syst. Des. 38(2), 97–118 (2011)CrossRefMATH Brim, L., Chaloupka, J., Doyen, L., Gentilini, R., Raskin, J.-F.: Faster algorithms for mean-payoff games. Formal Methods Syst. Des. 38(2), 97–118 (2011)CrossRefMATH
9.
10.
Zurück zum Zitat Chatterjee, K., Chmelik, M.: Indefinite-horizon reachability in Goal-DEC-POMDPs. In: Proceedings of ICAPS: International Conference on Automated Planning and Scheduling, pp. 88–96. AAAI Press (2016) Chatterjee, K., Chmelik, M.: Indefinite-horizon reachability in Goal-DEC-POMDPs. In: Proceedings of ICAPS: International Conference on Automated Planning and Scheduling, pp. 88–96. AAAI Press (2016)
11.
Zurück zum Zitat Chatterjee, K., Chmelik, M., Gupta, R., Kanodia, A.: Optimal cost almost-sure reachability in POMDPs. Artif. Intell. 234, 26–48 (2016)MathSciNetCrossRefMATH Chatterjee, K., Chmelik, M., Gupta, R., Kanodia, A.: Optimal cost almost-sure reachability in POMDPs. Artif. Intell. 234, 26–48 (2016)MathSciNetCrossRefMATH
12.
Zurück zum Zitat Chatterjee, K., Forejt, V., Wojtczak, D.: Multi-objective discounted reward verification in graphs and MDPs. In: McMillan, K., Middeldorp, A., Voronkov, A. (eds.) LPAR 2013. LNCS, vol. 8312, pp. 228–242. Springer, Heidelberg (2013). doi:10.1007/978-3-642-45221-5_17 CrossRef Chatterjee, K., Forejt, V., Wojtczak, D.: Multi-objective discounted reward verification in graphs and MDPs. In: McMillan, K., Middeldorp, A., Voronkov, A. (eds.) LPAR 2013. LNCS, vol. 8312, pp. 228–242. Springer, Heidelberg (2013). doi:10.​1007/​978-3-642-45221-5_​17 CrossRef
13.
Zurück zum Zitat Chatterjee, K., Majumdar, R., Henzinger, T.A.: Markov decision processes with multiple objectives. In: Durand, B., Thomas, W. (eds.) STACS 2006. LNCS, vol. 3884, pp. 325–336. Springer, Heidelberg (2006). doi:10.1007/11672142_26 CrossRef Chatterjee, K., Majumdar, R., Henzinger, T.A.: Markov decision processes with multiple objectives. In: Durand, B., Thomas, W. (eds.) STACS 2006. LNCS, vol. 3884, pp. 325–336. Springer, Heidelberg (2006). doi:10.​1007/​11672142_​26 CrossRef
14.
Zurück zum Zitat Chatterjee, K., Velner, Y.: Hyperplane Separation technique for multidimensional mean-payoff games. In: D’Argenio, P.R., Melgratti, H. (eds.) CONCUR 2013. LNCS, vol. 8052, pp. 500–515. Springer, Heidelberg (2013). doi:10.1007/978-3-642-40184-8_35 CrossRef Chatterjee, K., Velner, Y.: Hyperplane Separation technique for multidimensional mean-payoff games. In: D’Argenio, P.R., Melgratti, H. (eds.) CONCUR 2013. LNCS, vol. 8052, pp. 500–515. Springer, Heidelberg (2013). doi:10.​1007/​978-3-642-40184-8_​35 CrossRef
15.
Zurück zum Zitat Chen, T., Forejt, V., Kwiatkowska, M., Simaitis, A., Trivedi, A., Ummels, M.: Playing stochastic games precisely. In: Koutny, M., Ulidowski, I. (eds.) CONCUR 2012. LNCS, vol. 7454, pp. 348–363. Springer, Heidelberg (2012). doi:10.1007/978-3-642-32940-1_25 CrossRef Chen, T., Forejt, V., Kwiatkowska, M., Simaitis, A., Trivedi, A., Ummels, M.: Playing stochastic games precisely. In: Koutny, M., Ulidowski, I. (eds.) CONCUR 2012. LNCS, vol. 7454, pp. 348–363. Springer, Heidelberg (2012). doi:10.​1007/​978-3-642-32940-1_​25 CrossRef
16.
17.
Zurück zum Zitat Filar, J., Vrieze, K.: Competitive Markov Decision Processes. Springer-Verlag, Heidelberg (1997)MATH Filar, J., Vrieze, K.: Competitive Markov Decision Processes. Springer-Verlag, Heidelberg (1997)MATH
18.
Zurück zum Zitat Filiot, E., Gentilini, R., Raskin, J.-F.: Quantitative languages defined by functional automata. Logical Methods Comput. Sci. 11(3) (2015) Filiot, E., Gentilini, R., Raskin, J.-F.: Quantitative languages defined by functional automata. Logical Methods Comput. Sci. 11(3) (2015)
19.
Zurück zum Zitat Gurvich, V.A., Karzanov, A.V., Khachiyan, L.G.: Cyclic games and an algorithm to find minimax cycle means in directed graphs. USSR Comput. Math. Math. Phy. 28(5), 85–91 (1988)CrossRefMATH Gurvich, V.A., Karzanov, A.V., Khachiyan, L.G.: Cyclic games and an algorithm to find minimax cycle means in directed graphs. USSR Comput. Math. Math. Phy. 28(5), 85–91 (1988)CrossRefMATH
20.
Zurück zum Zitat Haase, C., Kreutzer, S., Ouaknine, J., Worrell, J.: Reachability in succinct and parametric one-counter automata. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009. LNCS, vol. 5710, pp. 369–383. Springer, Heidelberg (2009). doi:10.1007/978-3-642-04081-8_25 CrossRef Haase, C., Kreutzer, S., Ouaknine, J., Worrell, J.: Reachability in succinct and parametric one-counter automata. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009. LNCS, vol. 5710, pp. 369–383. Springer, Heidelberg (2009). doi:10.​1007/​978-3-642-04081-8_​25 CrossRef
21.
Zurück zum Zitat Hansen, T.D., Miltersen, P.B., Zwick, U.: Strategy iteration is strongly polynomial for 2-player turn-based stochastic games with a constant discount factor. J. ACM 60(1), 1:1–1:16 (2013)MathSciNetCrossRefMATH Hansen, T.D., Miltersen, P.B., Zwick, U.: Strategy iteration is strongly polynomial for 2-player turn-based stochastic games with a constant discount factor. J. ACM 60(1), 1:1–1:16 (2013)MathSciNetCrossRefMATH
23.
Zurück zum Zitat Hunter, P., Raskin, J.-F.: Quantitative games with interval objectives. In: Proceedings of FSTTCS, vol. 29 of LIPIcs, pp. 365–377. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2014) Hunter, P., Raskin, J.-F.: Quantitative games with interval objectives. In: Proceedings of FSTTCS, vol. 29 of LIPIcs, pp. 365–377. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2014)
24.
Zurück zum Zitat Jurdziński, M., Lazić, R., Schmitz, S.: Fixed-dimensional energy games are in pseudo-polynomial time. In: Halldórsson, M.M., Iwama, K., Kobayashi, N., Speckmann, B. (eds.) ICALP 2015. LNCS, vol. 9135, pp. 260–272. Springer, Heidelberg (2015). doi:10.1007/978-3-662-47666-6_21 CrossRef Jurdziński, M., Lazić, R., Schmitz, S.: Fixed-dimensional energy games are in pseudo-polynomial time. In: Halldórsson, M.M., Iwama, K., Kobayashi, N., Speckmann, B. (eds.) ICALP 2015. LNCS, vol. 9135, pp. 260–272. Springer, Heidelberg (2015). doi:10.​1007/​978-3-662-47666-6_​21 CrossRef
29.
Zurück zum Zitat Velner, Y., Chatterjee, K., Doyen, L., Henzinger, T.A., Rabinovich, A.M., Raskin, J.-F.: The complexity of multi-mean-payoff and multi-energy games. Inf. Comput. 241, 177–196 (2015)MathSciNetCrossRefMATH Velner, Y., Chatterjee, K., Doyen, L., Henzinger, T.A., Rabinovich, A.M., Raskin, J.-F.: The complexity of multi-mean-payoff and multi-energy games. Inf. Comput. 241, 177–196 (2015)MathSciNetCrossRefMATH
30.
Metadaten
Titel
The Cost of Exactness in Quantitative Reachability
verfasst von
Krishnendu Chatterjee
Laurent Doyen
Thomas A. Henzinger
Copyright-Jahr
2017
DOI
https://doi.org/10.1007/978-3-319-63121-9_18

Premium Partner