Abstract
Safety properties, which assert that the system always stays within some allowed region, have been extensively studied and used. In the last years, we see more and more research on quantitative formal methods, where systems and specifications are weighted. We introduce and study safety in the weighted setting. For a value v ∈ ℚ , we say that a weighted language L:Σ* → ℚ is v-safe if every word with cost at least v has a prefix all whose extensions have cost at least v. The language L is then weighted safe if L is v-safe for some v.
Given a regular weighted language L, we study the set of values v ∈ ℚ for which L is v-safe. We show that this set need not be closed upwards or downwards and we relate the v-safety of L with the safety of the (Boolean) language of words whose cost in L is at most v. We show that the latter need not be regular but is always context free. Given a deterministic weighted automaton \({\cal A}\), we relate the safety of \(L({\cal A})\) with the structure of \({\cal A}\), and we study the problem of deciding whether \(L({\cal A})\) is v-safe for a given v. We also study the weighted safety of \(L({\cal A})\) and provide bounds on the minimal value |v| for which a weighted language \(L({\cal A})\) is v-safe.
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References
Almagor, S., Boker, U., Kupferman, O.: What’s decidable about weighted automata? In: Bultan, T., Hsiung, P.-A. (eds.) ATVA 2011. LNCS, vol. 6996, pp. 482–491. Springer, Heidelberg (2011)
Almagor, S., Boker, U., Kupferman, O.: Formalizing and reasoning about quality. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds.) ICALP 2013, Part II. LNCS, vol. 7966, pp. 15–27. Springer, Heidelberg (2013)
Alpern, B., Schneider, F.B.: Recognizing safety and liveness. Distributed Computing 2, 117–126 (1987)
Aminof, B., Kupferman, O., Lampert, R.: Reasoning about online algorithms with weighted automata. ACM Transactions on Algorithms 6(2) (2010)
Baier, C., Bertrand, N.: M Grösser. Probabilistic automata over infinite words: Expressiveness, efficiency, and decidability. In: Proc. 11th DCFS, pp. 3–16 (2006)
Biere, A., Cimatti, A., Clarke, E., Zhu, Y.: Symbolic model checking without BDDs. In: Cleaveland, W.R. (ed.) TACAS/ETAPS 1999. LNCS, vol. 1579, pp. 193–207. Springer, Heidelberg (1999)
Bloem, R., Gabow, H.N., Somenzi, F.: An algorithm for strongly connected component analysis in n logn symbolic steps. In: Johnson, S.D., Hunt Jr., W.A. (eds.) FMCAD 2000. LNCS, vol. 1954, pp. 37–54. Springer, Heidelberg (2000)
Boker, U., Chatterjee, K., Henzinger, T.A., Kupferman, O.: Temporal specifications with accumulative values. In: Proc. 26th LICS, pp. 43–52 (2011)
Chatterjee, K., Doyen, L., Henzinger, T.A.: Quantitative languages. In: Kaminski, M., Martini, S. (eds.) CSL 2008. LNCS, vol. 5213, pp. 385–400. Springer, Heidelberg (2008)
Culik, K., Kari, J.: Digital images and formal languages. In: Handbook of Formal Languages, Beyond Words, vol. 3, pp. 599–616 (1997)
Erdös, P., Graham, R.L.: On a linear diophantine problem of frobenius. ActaArith 21, 399–408 (1972)
Filiot, E., Jin, N., Raskin, J.-F.: An antichain algorithm for LTL realizability. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 263–277. Springer, Heidelberg (2009)
Harel, D., Katz, G., Marron, A., Weiss, G.: Non-intrusive repair of reactive programs. In: ICECCS, pp. 3–12 (2012)
Havelund, K., Roşu, G.: Synthesizing monitors for safety properties. In: Katoen, J.-P., Stevens, P. (eds.) TACAS 2002. LNCS, vol. 2280, pp. 342–356. Springer, Heidelberg (2002)
Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley (1979)
Kupferman, O., Vardi, M.Y.: Model checking of safety properties. MFCS 19(3), 291–314 (2001)
Kupferman, O., Vardi, M.Y.: Synthesis of trigger properties. In: Clarke, E.M., Voronkov, A. (eds.) LPAR-16 2010. LNCS, vol. 6355, pp. 312–331. Springer, Heidelberg (2010)
Manna, Z., Pnueli, A.: The Temporal Logic of Reactive and Concurrent Systems: Specification. Springer (1992)
Manna, Z., Pnueli, A.: The Temporal Logic of Reactive and Concurrent Systems: Safety. Springer (1995)
Mohri, M.: Finite-state transducers in language and speech processing. Computational Linguistics 23(2), 269–311 (1997)
Mohri, M., Pereira, F.C.N., Riley, M.: Weighted finite-state transducers in speech recognition. Computer Speech and Language 16(1), 69–88 (2002)
Pnueli, A., Shahar, E.: Liveness and acceleration in parameterized verification. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 328–343. Springer, Heidelberg (2000)
Sistla, A.P.: Safety, liveness and fairness in temporal logic. FAC 6, 495–511 (1994)
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Weiner, S., Hasson, M., Kupferman, O., Pery, E., Shevach, Z. (2013). Weighted Safety. In: Van Hung, D., Ogawa, M. (eds) Automated Technology for Verification and Analysis. Lecture Notes in Computer Science, vol 8172. Springer, Cham. https://doi.org/10.1007/978-3-319-02444-8_11
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DOI: https://doi.org/10.1007/978-3-319-02444-8_11
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