Skip to main content
SpringerLink
Log in

Synthesis of Trigger Properties

  • Conference paper
Logic for Programming, Artificial Intelligence, and Reasoning (LPAR 2010)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6355))

Abstract

In automated synthesis, we transform a specification into a system that is guaranteed to satisfy the specification. In spite of the rich theory developed for temporal synthesis, little of this theory has been reduced to practice. This is in contrast with model-checking theory, which has led to industrial development and use of formal verification tools. We address this problem here by considering a certain class of PSL properties; this class covers most of the properties used in practice by system designers. We refer to this class as the class of trigger properties.

We show that the synthesis problem for trigger properties is more amenable to implementation than that of general PSL properties. While the problem is still 2EXPTIME-complete, it can be solved using techniques that are significantly simpler than the techniques used in general temporal synthesis. Not only can we avoid the use of Safra’s determinization, but we can also avoid the use of progress ranks. Rather, the techniques used are based on classical subset constructions. This makes our approach amenable also to symbolic implementation, as well as an incremental implementation, in which the specification evolves over time.

Work supported in part by NSF grant CCF-0728882, by BSF grant 9800096, and by gift from Intel. Part of this work was done while the second author was on sabbatical at the Hebrew University of Jerusalem.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Armoni, R., Fix, L., Flaisher, A., Gerth, R., Ginsburg, B., Kanza, T., Landver, A., Mador-Haim, S., Singerman, E., Tiemeyer, A., Vardi, M.Y., Zbar, Y.: The ForSpec temporal logic: A new temporal property-specification logic. In: Katoen, J.-P., Stevens, P. (eds.) TACAS 2002. LNCS, vol. 2280, pp. 196–211. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  2. Abadi, M., Lamport, L., Wolper, P.: Realizable and unrealizable concurrent program specifications. In: Ronchi Della Rocca, S., Ausiello, G., Dezani-Ciancaglini, M. (eds.) ICALP 1989. LNCS, vol. 372, pp. 1–17. Springer, Heidelberg (1989)

    Chapter  Google Scholar 

  3. Asarin, E., Maler, O., Pnueli, A., Sifakis, J.: Controller synthesis for timed automata. In: IFAC Symposium on System Structure and Control, pp. 469–474. Elsevier, Amsterdam (1998)

    Google Scholar 

  4. Alur, R., La Torre, S.: Deterministic generators and games for ltl fragments. ACM Transactions on Computational Logic 5(1), 1–25 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  5. Althoff, C.S., Thomas, W., Wallmeier, N.: Observations on determinization of Büchi automata. In: Farré, J., Litovsky, I., Schmitz, S. (eds.) CIAA 2005. LNCS, vol. 3845, pp. 262–272. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  6. Beer, I., Ben-David, S., Eisner, C., Fisman, D., Gringauze, A., Rodeh, Y.: The temporal logic Sugar. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 363–367. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  7. Basin, D.A., Deville, Y., Flener, P., Hamfelt, A., Nilsson, J.F.: Synthesis of programs in computational logic. In: Bruynooghe, M., Lau, K.-K. (eds.) Program Development in Computational Logic. LNCS, vol. 3049, pp. 30–65. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  8. Bustan, D., Flaisher, A., Grumberg, O., Kupferman, O., Vardi, M.Y.: Regular vacuity. In: Borrione, D., Paul, W. (eds.) CHARME 2005. LNCS, vol. 3725, pp. 191–206. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  9. Bloem, R., Galler, S., Jobstmann, B., Piterman, N., Pnueli, A., Weiglhofer, M.: Automatic hardware synthesis from specifications: a case study. In: Proc. Conference on Design, Automation and Test in Europe, pp. 1188–1193. ACM, New York (2007)

    Google Scholar 

  10. Büchi, J.R., Landweber, L.H.: Solving sequential conditions by finite-state strategies. Trans. AMS 138, 295–311 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  11. Clarke, E.M., Grumberg, O., Peled, D.: Model Checking. MIT Press, Cambridge (1999)

    Google Scholar 

  12. Choueka, Y.: Theories of automata on ω-tapes: A simplified approach. Journal of Computer and Systems Science 8, 117–141 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  13. Church, A.: Logic, arithmetics, and automata. In: Proc. Int. Congress of Mathematicians, 1962, pp. 23–35. Institut Mittag-Leffler (1963)

    Google Scholar 

  14. Chandra, A.K., Kozen, D.C., Stockmeyer, L.J.: Alternation. Journal of the Association for Computing Machinery 28(1), 114–133 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  15. Dill, D.L.: Trace theory for automatic hierarchical verification of speed independent circuits. MIT Press, Cambridge (1989)

    Google Scholar 

  16. Doyen, L., Raskin, J.-F.: Antichains for the automata-based approach to model-checking. Logical Methods in Computer Science 5(1) (2009)

    Google Scholar 

  17. Emerson, E.A., Clarke, E.M.: Using branching time logic to synthesize synchronization skeletons. Science of Computer Programming 2, 241–266 (1982)

    Article  MATH  Google Scholar 

  18. Eisner, C., Fisman, D.: A Practical Introduction to PSL. Springer, Heidelberg (2006)

    Google Scholar 

  19. Elgaard, J., Klarlund, N., Möller, A.: Mona 1.x: new techniques for WS1S and WS2S. In: Vardi, M.Y. (ed.) CAV 1998. LNCS, vol. 1427, pp. 516–520. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  20. Emerson, E.A., Lei, C.-L.: Efficient model checking in fragments of the propositional μ-calculus. In: Proc. 1st IEEE Symp. on Logic in Computer Science, pp. 267–278 (1986)

    Google Scholar 

  21. Harding, A., Ryan, M., Schobbens, P.: A new algorithm for strategy synthesis in LTL games. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 477–492. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  22. Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading (1979)

    MATH  Google Scholar 

  23. Jurdzinski, M.: Small progress measures for solving parity games. In: Reichel, H., Tison, S. (eds.) STACS 2000. LNCS, vol. 1770, pp. 290–301. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  24. Klarlund, N.: Mona & Fido: The logic-automaton connection in practice. In: Nielsen, M. (ed.) CSL 1997. LNCS, vol. 1414. Springer, Heidelberg (1998)

    Google Scholar 

  25. Kupferman, O., Piterman, N., Vardi, M.Y.: Safraless compositional synthesis. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 31–44. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  26. Kupferman, O., Vardi, M.Y.: Freedom, weakness, and determinism: from linear-time to branching-time. In: Proc. 13th IEEE Symp. on Logic in Computer Science, pp. 81–92 (1998)

    Google Scholar 

  27. Kupferman, O., Vardi, M.Y.: Weak alternating automata and tree automata emptiness. In: Proc. 30th ACM Symp. on Theory of Computing, pp. 224–233 (1998)

    Google Scholar 

  28. Kupferman, O., Vardi, M.Y.: Synthesis with incomplete information. In: Advances in Temporal Logic, pp. 109–127. Kluwer Academic Publishers, Dordrecht (2000)

    Chapter  Google Scholar 

  29. Kupferman, O., Vardi, M.Y.: Complementation constructions for nondeterministic automata on infinite words. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 206–221. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  30. Kupferman, O., Vardi, M.Y.: From linear time to branching time. ACM Transactions on Computational Logic 6(2), 273–294 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  31. Kupferman, O., Vardi, M.Y.: Safraless decision procedures. In: Proc. 46th IEEE Symp. on Foundations of Computer Science, pp. 531–540 (2005)

    Google Scholar 

  32. Lichtenstein, O., Pnueli, A.: Checking that finite state concurrent programs satisfy their linear specification. In: Proc. 12th ACM Symp. on Principles of Programming Languages, pp. 97–107 (1985)

    Google Scholar 

  33. Miyano, S., Hayashi, T.: Alternating finite automata on ω-words. Theoretical Computer Science 32, 321–330 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  34. Morgenstern, A., Schneider, K.: From ltl to symbolically represented deterministic automata. In: Logozzo, F., Peled, D.A., Zuck, L.D. (eds.) VMCAI 2008. LNCS, vol. 4905, pp. 279–293. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  35. Morgenstern, A., Schneider, K.: Generating deterministic ω-automata for most LTL formulas by the breakpoint construction. In: Methoden und Beschreibungssprachen zur Modellierung und Verifikation von Schaltungen und Systemen, Freiburg, Germany (2008)

    Google Scholar 

  36. Manna, Z., Waldinger, R.: A deductive approach to program synthesis. ACM Transactions on Programming Languagues and Systems 2(1), 90–121 (1980)

    Article  MATH  Google Scholar 

  37. Manna, Z., Wolper, P.: Synthesis of communicating processes from temporal logic specifications. ACM Transactions on Programming Languagues and Systems 6(1), 68–93 (1984)

    Article  MATH  Google Scholar 

  38. Piterman, N.: From nondeterministic Büchi and Streett automata to deterministic parity automata. Logical Methods in Computer Science 3(3), 5 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  39. Pnueli, A.: The temporal logic of programs. In: Proc. 18th IEEE Symp. on Foundations of Computer Science, pp. 46–57 (1977)

    Google Scholar 

  40. Piterman, N., Pnueli, A., Saar, Y.: Synthesis of reactive(1) designs. In: Emerson, E.A., Namjoshi, K.S. (eds.) VMCAI 2006. LNCS, vol. 3855, pp. 364–380. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  41. Pnueli, A., Rosner, R.: On the synthesis of a reactive module. In: Proc. 16th ACM Symp. on Principles of Programming Languages, pp. 179–190 (1989)

    Google Scholar 

  42. Pnueli, A., Rosner, R.: On the synthesis of an asynchronous reactive module. In: Ronchi Della Rocca, S., Ausiello, G., Dezani-Ciancaglini, M. (eds.) ICALP 1989. LNCS, vol. 372, pp. 652–671. Springer, Heidelberg (1989)

    Chapter  Google Scholar 

  43. Rabin, M.O.: Automata on infinite objects and Church’s problem. Amer. Mathematical Society, Providence (1972)

    Book  MATH  Google Scholar 

  44. Rosner, R.: Modular Synthesis of Reactive Systems. PhD thesis, Weizmann Institute of Science (1992)

    Google Scholar 

  45. Rabin, M.O., Scott, D.: Finite automata and their decision problems. IBM Journal of Research and Development 3, 115–125 (1959)

    Article  MathSciNet  MATH  Google Scholar 

  46. Shimizu, K., Dill, D.L., Chou, C.-T.: A specification methodology by a collection of compact properties as applied to the intel itanium processor bus protocol. In: Margaria, T., Melham, T.F. (eds.) CHARME 2001. LNCS, vol. 2144, pp. 340–354. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  47. Tasiran, S., Hojati, R., Brayton, R.K.: Language containment using non-deterministic omega-automata. In: Camurati, P.E., Eveking, H. (eds.) CHARME 1995. LNCS, vol. 987, pp. 261–277. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  48. Tabakov, D., Vardi, M.Y.: Model checking Büechi specifications. In: 1st International Conference on Language and Automata Theory and Application Principles of Programming Languages (2007)

    Google Scholar 

  49. Vardi, M.Y.: An automata-theoretic approach to fair realizability and synthesis. In: Wolper, P. (ed.) CAV 1995. LNCS, vol. 939, pp. 267–292. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  50. Vijayaraghavan, S., Ramanathan, M.: A Practical Guide for SystemVerilog Assertions. Springer, Heidelberg (2005)

    Google Scholar 

  51. Vardi, M.Y., Stockmeyer, L.: Improved upper and lower bounds for modal logics of programs. In: Proc. 17th ACM Symp. on Theory of Computing, pp. 240–251 (1985)

    Google Scholar 

  52. Vardi, M.Y., Wolper, P.: Automata-theoretic techniques for modal logics of programs. Journal of Computer and Systems Science 32(2), 182–221 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  53. Vardi, M.Y., Wolper, P.: Reasoning about infinite computations. Information and Computation 115(1), 1–37 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  54. Wong-Toi, H., Dill, D.L.: Synthesizing processes and schedulers from temporal specifications. In: Clarke, E.M., Kurshan, R.P. (eds.) Proc. 2nd Int. Conf. on Computer Aided Verification. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 3, pp. 177–186. AMS, Providence (1991)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Engineering and Computer Science, Hebrew University, Jerusalem, 91904, Israel

    Orna Kupferman

  2. Department of Computer Science, Rice University, Houston, TX, 77251-1892, U.S.A.

    Moshe Y. Vardi

Authors
  1. Orna Kupferman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Moshe Y. Vardi
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Carnegie Mellon University, USA

    Edmund M. Clarke

  2. School of Computer Science, University of Manchester, Kilburn Building, Oxford Road, M13 9PL, Manchester, UK

    Andrei Voronkov

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kupferman, O., Vardi, M.Y. (2010). Synthesis of Trigger Properties. In: Clarke, E.M., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2010. Lecture Notes in Computer Science(), vol 6355. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17511-4_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-17511-4_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17510-7

  • Online ISBN: 978-3-642-17511-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation