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Formal Reasoning on Infinite Data Values: An Ongoing Quest

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Engineering Trustworthy Software Systems (SETSS 2016)

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Abstract

With motivations from formal verification and databases, formal models to reason about software systems that contain data values from an infinite domain became a research focus in theoretical computer science community during the last decade. In this chapter, we present a tutorial to summarise the state of the art of these formal models. We focus on automata models and logics. We organise the models according to the different approaches to deal with the data values from an infinite domain. Specifically, we present the following models, register automata (and related logics), data automata (and related logics), pebble automata, and symbolic automata and transducers. In addition, we also incorporate two application-oriented sections, respectively on formal models to reason about programs manipulating dynamic data structures, and on formal models for the static analysis of data-parallel programs. For these two sections, we choose to present separation logic with data constraints, logic of graph reachability and stratified sets, streaming transducers, and streaming numerical transducers. For each model, we introduce the basic definitions, use some examples to illustrate the model, and state the main theoretical properties of the model. We hope that this tutorial will be useful if one wants to have a bird’s eye of view on this field and know the basic concepts underlying those models.

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Notes

  1. 1.

    The notion of stratified sets comes from [Zar03].

  2. 2.

    http://hadoop.apache.com.

  3. 3.

    http://spark.apache.com.

References

  1. Alur, R., Cerný, P.: Expressiveness of streaming string transducers. In: Proceedings of the 30th Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS), Leibniz International Proceedings in Informatics (LIPIcs), vol. 8, pp. 1–12 (2010)

    Google Scholar 

  2. Alur, R., Cerny, P.: Streaming transducers for algorithmic verification of single-pass list-processing programs. In: Proceedings of the 38th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL), pp. 599–610 (2011)

    Google Scholar 

  3. Alur, R., Cerný, P., Weinstein, S.: Algorithmic analysis of array-accessing programs. ACM Trans. Comput. Log. 13(3), 27 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  4. Alur, R., D’Antoni, L.: Streaming tree transducers. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds.) ICALP 2012. LNCS, vol. 7392, pp. 42–53. Springer, Heidelberg (2012). doi:10.1007/978-3-642-31585-5_8

    Chapter  Google Scholar 

  5. Alur, R., Durand-Gasselin, A., Trivedi, A.: From monadic second-order definable string transformations to transducers. In: Proceedings of the 28th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), pp. 458–467 (2013)

    Google Scholar 

  6. Antonopoulos, T., Gorogiannis, N., Haase, C., Kanovich, M., Ouaknine, J.: Foundations for decision problems in separation logic with general inductive predicates. In: Muscholl, A. (ed.) FoSSaCS 2014. LNCS, vol. 8412, pp. 411–425. Springer, Heidelberg (2014). doi:10.1007/978-3-642-54830-7_27

    Chapter  Google Scholar 

  7. Abdulla, P.A., Holik, L., Jonsson, B., Lengal, O., Trinh, C.Q., Vojnar, T.: Verification of heap manipulating programs with ordered data by extended forest automata. In: Proceedings of the 11th International Symposium on Automated Technology for Verification and Analysis (ATVA), pp. 224–239 (2013)

    Google Scholar 

  8. Bansal, K., Brochenin, R., Lozes, E.: Beyond shapes: lists with ordered data. In: de Alfaro, L. (ed.) FoSSaCS 2009. LNCS, vol. 5504, pp. 425–439. Springer, Heidelberg (2009). doi:10.1007/978-3-642-00596-1_30

    Chapter  Google Scholar 

  9. Berdine, J., Calcagno, C., O’Hearn, P.W.: Symbolic execution with separation logic. In: Yi, K. (ed.) APLAS 2005. LNCS, vol. 3780, pp. 52–68. Springer, Heidelberg (2005). doi:10.1007/11575467_5

    Chapter  Google Scholar 

  10. Bouajjani, A., Drăgoi, C., Enea, C., Sighireanu, M.: A logic-based framework for reasoning about composite data structures. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009. LNCS, vol. 5710, pp. 178–195. Springer, Heidelberg (2009). doi:10.1007/978-3-642-04081-8_13

    Chapter  Google Scholar 

  11. Bouajjani, A., Drǎgoi, C., Enea, C., Sighireanu, M.: Accurate invariant checking for programs manipulating lists and arrays with infinite data. In: Chakraborty, S., Mukund, M. (eds.) ATVA 2012. LNCS, vol. 7561, pp. 167–182. Springer, Heidelberg (2012). doi:10.1007/978-3-642-33386-6_14

    Chapter  Google Scholar 

  12. Bojanczyk, M., David, C., Muscholl, A., Schwentick, T., Segoufin, L.: Two-variable logic on data words. ACM Trans. Comput. Logic 12(4), 27 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  13. Brotherston, J., Fuhs, C., Gorogiannis, J.N., Perez, A.N.: A decision procedure for satisfiability in separation logic with inductive predicates. In: Proceedings of the 29th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) (2014)

    Google Scholar 

  14. Bojańczyk, M., Klin, B., Lasota, S., Toruńczyk, S.: Turing machines with atoms. In: Proceedings of the 28th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), pp. 183–192 (2013)

    Google Scholar 

  15. Bojanczyk, M., Lasota, S.: An extension of data automata that captures XPath. Log. Methods Comput. Sci. 8(1), 1–28 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  16. Bojanczyk, M., Muscholl, A., Schwentick, T., Segoufin, L., David, C.: Two-variable logic on words with data. In: Proceedings of the 21th IEEE Symposium on Logic in Computer Science (LICS), pp. 7–16 (2006)

    Google Scholar 

  17. Bojańczyk, M.: Modelling infinite structures with atoms. In: Libkin, L., Kohlenbach, U., de Queiroz, R. (eds.) WoLLIC 2013. LNCS, vol. 8071, pp. 13–28. Springer, Heidelberg (2013). doi:10.1007/978-3-642-39992-3_3

    Google Scholar 

  18. Björklund, H., Schwentick, T.: On notions of regularity for data languages. Theor. Comput. Sci. 411(4–5), 702–715 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  19. Bojańczyk, M., Samuelides, M., Schwentick, T., Segoufin, L.: Expressive power of pebble automata. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4051, pp. 157–168. Springer, Heidelberg (2006). doi:10.1007/11786986_15

    Chapter  Google Scholar 

  20. Büchi, J.R.: Weak second-order arithmetic and finite automata. Z. Math. Log. Grundl. Math. 6, 66–92 (1960)

    Article  MathSciNet  MATH  Google Scholar 

  21. Büchi, J.R.: On a decision method in restricted second-order arithmetic. In: Proceedings of the 1960 International Congress for Logic, Methodology and Philosophy of Science, pp. 1–11. Stanford University Press (1962)

    Google Scholar 

  22. Chin, W.-N., David, C., Nguyen, H.H., Qin, S.: Automated verification of shape, size and bag properties via user-defined predicates in separation logic. Sci. Comput. Program. 77(9), 1006–1036 (2012)

    Article  MATH  Google Scholar 

  23. Calcagno, C., Distefano, D., O’Hearn, P.W., Yang, H.: Compositional shape analysis by means of bi-abduction. J. ACM 58(6), 26:1–26:66 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  24. Cook, B., Haase, C., Ouaknine, J., Parkinson, M., Worrell, J.: Tractable reasoning in a fragment of separation logic. In: Katoen, J.-P., König, B. (eds.) CONCUR 2011. LNCS, vol. 6901, pp. 235–249. Springer, Heidelberg (2011). doi:10.1007/978-3-642-23217-6_16

    Chapter  Google Scholar 

  25. Chen, Y.-F., Hong, C.-D., Sinha, N., Wang, B.-Y.: Commutativity of reducers. In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 131–146. Springer, Heidelberg (2015). doi:10.1007/978-3-662-46681-0_9

    Google Scholar 

  26. Chaiken, R., Jenkins, B., Larson, P.Å., Ramsey, B., Shakib, D., Weaver, S., Zhou, J.: SCOPE: easy and efficient parallel processing of massive data sets. PVLDB 1(2), 1265–1276 (2008)

    Google Scholar 

  27. Cheng, E.Y.C., Kaminski, M.: Context-free languages over infinite alphabets. Acta Inf. 35(3), 245–267 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  28. Chen, Y.-F., Lengal, O., Tan, T., Wu, Z.: Equivalence of streaming numerical transducers (2016). (manuscript)

    Google Scholar 

  29. Chen, Y.-F., Song, L., Wu, Z.: The commutativity problem of the MapReduce framework: a transducer-based approach. In: Chaudhuri, S., Farzan, A. (eds.) CAV 2016. LNCS, vol. 9780, pp. 91–111. Springer, Cham (2016). doi:10.1007/978-3-319-41540-6_6

    Google Scholar 

  30. D’Antoni, L.: In the maze of data languages. CoRR, abs/1208.5980 (2012)

    Google Scholar 

  31. D’Antoni, L., Alur, R.: Symbolic visibly pushdown automata. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 209–225. Springer, Cham (2014). doi:10.1007/978-3-319-08867-9_14

    Google Scholar 

  32. Dean, J., Ghemawat, S.: MapReduce: simplified data processing on large clusters. In: Proceedings of the 6th Symposium on Operating System Design and Implementation (OSDI), pp. 137–150 (2004)

    Google Scholar 

  33. Decker, N., Habermehl, P., Leucker, M., Thoma, D.: Ordered navigation on multi-attributed data words. In: Baldan, P., Gorla, D. (eds.) CONCUR 2014. LNCS, vol. 8704, pp. 497–511. Springer, Heidelberg (2014). doi:10.1007/978-3-662-44584-6_34

    Google Scholar 

  34. Demri, S., Lazic, R.: LTL with the freeze quantifier and register automata. ACM Trans. Comput. Log. 10(3), 16:1–16:30 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  35. Distefano, D., O’Hearn, P.W., Yang, H.: A local shape analysis based on separation logic. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006. LNCS, vol. 3920, pp. 287–302. Springer, Heidelberg (2006). doi:10.1007/11691372_19

    Chapter  Google Scholar 

  36. D’Antoni, L., Veanes, M.: Minimization of symbolic automata. In: Proceedings of the 41st Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL), pp. 541–554 (2014)

    Google Scholar 

  37. D’Antoni, L., Veanes, M.: Extended symbolic finite automata and transducers. Form. Methods Syst. Des. 47(1), 93–119 (2015)

    Article  MATH  Google Scholar 

  38. Elgot, C.: Decision problems of finite automata design and related arithmetic. Trans. Am. Math. Soc. 98, 21–52 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  39. Enea, C., Sighireanu, M., Wu, Z.: On automated lemma generation for separation logic with inductive definitions. In: Finkbeiner, B., Pu, G., Zhang, L. (eds.) ATVA 2015. LNCS, vol. 9364, pp. 80–96. Springer, Cham (2015). doi:10.1007/978-3-319-24953-7_7

    Chapter  Google Scholar 

  40. Figueira, D.: Alternating register automata on finite words and trees. Log. Methods Comput. Sci. 8(1), 1–43 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  41. Fülöp, Z., Vogler, H.: Syntax-Directed Semantics - Formal Models Based on Tree Transducers. Monographs in Theoretical Computer Science. An EATCS Series. Springer, Heidelberg (1998)

    Book  MATH  Google Scholar 

  42. Fülöp, Z., Vogler, H.: Forward and backward application of symbolic tree transducers. Acta Inf. 51(5), 297–325 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  43. Gallier, J.H.: Logic for Computer Science: Foundations of Automatic Theorem Proving. Harper & Row Publishers, Inc., New York (1985)

    MATH  Google Scholar 

  44. Gu, X., Chen, T., Wu, Z.: A complete decision procedure for linearly compositional separation logic with data constraints. In: Olivetti, N., Tiwari, A. (eds.) IJCAR 2016. LNCS (LNAI), vol. 9706, pp. 532–549. Springer, Cham (2016). doi:10.1007/978-3-319-40229-1_36

    Google Scholar 

  45. Grumberg, O., Kupferman, O., Sheinvald, S.: Variable automata over infinite alphabets. In: Dediu, A.-H., Fernau, H., Martín-Vide, C. (eds.) LATA 2010. LNCS, vol. 6031, pp. 561–572. Springer, Heidelberg (2010). doi:10.1007/978-3-642-13089-2_47

    Chapter  Google Scholar 

  46. Grumberg, O., Kupferman, O., Sheinvald, S.: Model checking systems and specifications with parameterized atomic propositions. In: Chakraborty, S., Mukund, M. (eds.) ATVA 2012. LNCS, vol. 7561, pp. 122–136. Springer, Heidelberg (2012). doi:10.1007/978-3-642-33386-6_11

    Chapter  Google Scholar 

  47. Grumberg, O., Kupferman, O., Sheinvald, S.: An automata-theoretic approach to reasoning about parameterized systems and specifications. In: Hung, D., Ogawa, M. (eds.) ATVA 2013. LNCS, vol. 8172, pp. 397–411. Springer, Heidelberg (2013). doi:10.1007/978-3-319-02444-8_28

    Chapter  Google Scholar 

  48. Grumberg, O., Kupferman, O., Sheinvald, S.: A game-theoretic approach to simulation of data-parameterized systems. In: Cassez, F., Raskin, J.-F. (eds.) ATVA 2014. LNCS, vol. 8837, pp. 348–363. Springer, Heidelberg (2014). doi:10.1007/978-3-319-11936-6_25

    Google Scholar 

  49. German, S.M., Sistla, A.P.: Reasoning about systems with many processes. J. ACM 39(3), 675–735 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  50. Habermehl, P., Holík, L., Rogalewicz, A., Šimáček, J., Vojnar, T.: Forest automata for verification of heap manipulation. Form. Methods Syst. Des. 41(1), 83–106 (2012)

    Article  MATH  Google Scholar 

  51. Hofman, P., Lasota, S., Lazić, R., Leroux, J., Schmitz, S., Totzke, P.: Coverability trees for petri nets with unordered data. In: Jacobs, B., Löding, C. (eds.) FoSSaCS 2016. LNCS, vol. 9634, pp. 445–461. Springer, Heidelberg (2016). doi:10.1007/978-3-662-49630-5_26

    Chapter  Google Scholar 

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

    MATH  Google Scholar 

  53. Ihlemann, C., Jacobs, S., Sofronie-Stokkermans, V.: On local reasoning in verification. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 265–281. Springer, Heidelberg (2008). doi:10.1007/978-3-540-78800-3_19

    Chapter  Google Scholar 

  54. Kara, A.: Logics on data words: expressivity, satisfiability, model checking. Ph.D. thesis, TU Dortmund University (2016). https://eldorado.tu-dortmund.de/bitstream/2003/35216/1/Dissertation.pdf

  55. Kaminski, M., Francez, N.: Finite-memory automata. Theor. Comput. Sci. 134(2), 329–363 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  56. Kara, A., Schwentick, T., Tan, T.: Feasible automata for two-variable logic with successor on data words. In: Dediu, A.-H., Martín-Vide, C. (eds.) LATA 2012. LNCS, vol. 7183, pp. 351–362. Springer, Heidelberg (2012). doi:10.1007/978-3-642-28332-1_30

    Chapter  Google Scholar 

  57. Kaminski, M., Tan, T.: Regular expressions for languages over infinite alphabets. Fundam. Inform. 69(3), 301–318 (2006)

    MathSciNet  MATH  Google Scholar 

  58. Kaminski, M., Tan, T.: A note on two-pebble automata over infinite alphabets. Fundam. Inform. 98(4), 379–390 (2010)

    MathSciNet  MATH  Google Scholar 

  59. Le, Q.L., Sun, J., Chin, W.-N.: Satisfiability modulo heap-based programs. In: Chaudhuri, S., Farzan, A. (eds.) CAV 2016. LNCS, vol. 9779, pp. 382–404. Springer, Cham (2016). doi:10.1007/978-3-319-41528-4_21

    Google Scholar 

  60. Libkin, L., Tan, T., Vrgoc, D.: Regular expressions for data words. J. Comput. Syst. Sci. 81(7), 1278–1297 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  61. McNaughton, R., Papert, S.: Counter-Free Automata. MIT Press, Cambridge (1971)

    MATH  Google Scholar 

  62. Madhusudan, P., Parlato, G., Qiu, X.: Decidable logics combining heap structures and data. In: Proceedings of the 38th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL), pp. 611–622 (2011)

    Google Scholar 

  63. Manuel, A., Ramanujam, R.: Class counting automata on datawords. Int. J. Found. Comput. Sci. 22(4), 863–882 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  64. Mens, I.-E., Rahonis, G.: Variable tree automata over infinite ranked alphabets. In: Winkler, F. (ed.) CAI 2011. LNCS, vol. 6742, pp. 247–260. Springer, Heidelberg (2011). doi:10.1007/978-3-642-21493-6_16

    Chapter  Google Scholar 

  65. Murawski, A.S., Ramsay, S.J., Tzevelekos, N.: Reachability in pushdown register automata. In: Csuhaj-Varjú, E., Dietzfelbinger, M., Ésik, Z. (eds.) MFCS 2014. LNCS, vol. 8634, pp. 464–473. Springer, Heidelberg (2014). doi:10.1007/978-3-662-44522-8_39

    Google Scholar 

  66. Müller-Olm, M., Seidl, H.: A note on Karr’s algorithm. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 1016–1028. Springer, Heidelberg (2004). doi:10.1007/978-3-540-27836-8_85

    Chapter  Google Scholar 

  67. Nelson, G., Oppen, D.C.: Simplification by cooperating decision procedures. ACM Trans. Program. Lang. Syst. 1(2), 245–257 (1979)

    Article  MATH  Google Scholar 

  68. Neven, F., Schweikardt, N., Servais, F., Tan, T.: Distributed streaming with finite memory. In: Proceedings of the 18th International Conference on Database Theory (ICDT), pp. 324–341 (2015)

    Google Scholar 

  69. Neven, F., Schwentick, T., Vianu, V.: Towards regular languages over infinite alphabets. In: Sgall, J., Pultr, A., Kolman, P. (eds.) MFCS 2001. LNCS, vol. 2136, pp. 560–572. Springer, Heidelberg (2001). doi:10.1007/3-540-44683-4_49

    Chapter  Google Scholar 

  70. Neven, F., Schwentick, T., Vianu, V.: Finite state machines for strings over infinite alphabets. ACM Trans. Comput. Log. 5(3), 403–435 (2004)

    Article  MathSciNet  Google Scholar 

  71. Olston, C., Reed, B., Srivastava, U., Kumar, R., Tomkins, A.: Pig latin: a not-so-foreign language for data processing. In: Proceedings of the ACM SIGMOD International Conference on Management of Data (SIGMOD), pp. 1099–1110 (2008)

    Google Scholar 

  72. Piskac, R., Wies, T., Zufferey, D.: Automating separation logic using SMT. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 773–789. Springer, Heidelberg (2013). doi:10.1007/978-3-642-39799-8_54

    Chapter  Google Scholar 

  73. Piskac, R., Wies, T., Zufferey, D.: Automating separation logic with trees and data. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 711–728. Springer, Cham (2014). doi:10.1007/978-3-319-08867-9_47

    Google Scholar 

  74. Reynolds, J.C.: Separation logic: a logic for shared mutable data structures. In: Proceedings of the 17th IEEE Symposium on Logic in Computer Science (LICS), pp. 55–74 (2002)

    Google Scholar 

  75. Reynolds, A., Iosif, R., Serban, C., King, T.: A decision procedure for separation logic in SMT. In: Artho, C., Legay, A., Peled, D. (eds.) ATVA 2016. LNCS, vol. 9938, pp. 244–261. Springer, Cham (2016). doi:10.1007/978-3-319-46520-3_16

    Chapter  Google Scholar 

  76. Schützenberger, M.P.: On finite monoids having only trivial subgroups. Inf. Control 8(2), 190–194 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  77. Segoufin, L.: Automata and logics for words and trees over an infinite alphabet. In: Ésik, Z. (ed.) CSL 2006. LNCS, vol. 4207, pp. 41–57. Springer, Heidelberg (2006). doi:10.1007/11874683_3

    Chapter  Google Scholar 

  78. Sistla, A.P., German, S.M.: Reasoning with many processes. In: Proceedings of the 2nd Symposium on Logic in Computer Science (LICS), pp. 138–152 (1987)

    Google Scholar 

  79. Sagiv, M., Reps, T., Wilhelm, R.: Parametric shape analysis via 3-valued logic. ACM Trans. Program. Lang. Syst. 24(3), 217–298 (2002)

    Article  Google Scholar 

  80. Song, F., Wu, Z.: Extending temporal logics with data variable quantifications. In: Proceedings of the 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS), pp. 253–265 (2014)

    Google Scholar 

  81. Song, F., Zhilin, W.: On temporal logics with data variable quantifications: decidability and complexity. Inf. Comput. 251, 104–139 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  82. Tan, T.: On pebble automata for data languages with decidable emptiness problem. J. Comput. Syst. Sci. 76(8), 778–791 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  83. Tan, T.: Graph reachability and pebble automata over infinite alphabets. ACM Trans. Comput. Log. 14(3), 19 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  84. Tan, T.: Extending two-variable logic on data trees with order on data values and its automata. ACM Trans. Comput. Log. 15(1), 8 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  85. Thusoo, A., Sarma, J.S., Jain, N., Shao, Z., Chakka, P., Anthony, S., Liu, H., Wyckoff, P., Murthy, R.: Hive - a warehousing solution over a map-reduce framework. PVLDB 2(2), 1626–1629 (2009)

    Google Scholar 

  86. Thatcher, J.W., Wright, J.B.: Generalized finite automata theory with an application to a decision problem of second-order logic. Theory Comput. Syst. 2, 57–81 (1968)

    MathSciNet  MATH  Google Scholar 

  87. Veanes, M., Bjørner, N.: Foundations of finite symbolic tree transducers. Bull. EATCS 105, 141–173 (2011)

    MathSciNet  MATH  Google Scholar 

  88. Veanes, M., Bjørner, N.: Symbolic tree transducers. In: Clarke, E., Virbitskaite, I., Voronkov, A. (eds.) PSI 2011. LNCS, vol. 7162, pp. 377–393. Springer, Heidelberg (2012). doi:10.1007/978-3-642-29709-0_32

    Chapter  Google Scholar 

  89. Veanes, M., Bjørner, N.: Symbolic tree automata. Inf. Process. Lett. 115(3), 418–424 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  90. Veanes, M., Bjørner, N.: Equivalence of finite-valued symbolic finite transducers. In: Mazzara, M., Voronkov, A. (eds.) PSI 2015. LNCS, vol. 9609, pp. 276–290. Springer, Cham (2016). doi:10.1007/978-3-319-41579-6_21

    Chapter  Google Scholar 

  91. Veanes, M., Bjørner, N., Nachmanson, L., Bereg, S.: Monadic decomposition. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 628–645. Springer, Cham (2014). doi:10.1007/978-3-319-08867-9_42

    Google Scholar 

  92. Veanes, M., D’Antoni, L.: Minimization of symbolic tree automata. In: Proceedings of the 30th IEEE Symposium on Logic in Computer Science (LICS) (2016)

    Google Scholar 

  93. Veanes, M.: Applications of symbolic finite automata. In: Konstantinidis, S. (ed.) CIAA 2013. LNCS, vol. 7982, pp. 16–23. Springer, Heidelberg (2013). doi:10.1007/978-3-642-39274-0_3

    Chapter  Google Scholar 

  94. Veanes, M., Hooimeijer, P., Livshits, B., Molnar, D., Bjørner, N.: Symbolic finite state transducers: algorithms and applications. In: Proceedings of the 39th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL), pp. 137–150 (2012)

    Google Scholar 

  95. Vianu, V.: Automatic verification of database-driven systems: a new frontier. In: Proceedings of the 12th International Conference on Database Theory (ICDT), pp. 1–13 (2009)

    Google Scholar 

  96. van Leeuwen, J. (ed.): Handbook of Theoretical Computer Science. Formal Models and Semantics, vol. B. Elsevier and MIT Press, Amsterdam and Cambridge (1990)

    MATH  Google Scholar 

  97. van Noord, G., Gerdemann, D.: Finite state transducers with predicates and identities. Grammars 4(3), 263–286 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  98. Vardi, M.Y., Wolper, P.: An automata-theoretic approach to automatic program verification (preliminary report). In: Proceedings of the 1st Symposium on Logic in Computer Science (LICS), pp. 332–344 (1986)

    Google Scholar 

  99. Watson, B.W.: Implementing and using finite automata toolkits. Nat. Lang. Eng. 2(4), 295–302 (1996)

    Article  Google Scholar 

  100. Wu, Z.: A decidable extension of data automata. In: Proceedings of the 2nd International Symposium on Games, Automata, Logics and Formal Verification (GandALF), pp. 116–130 (2011)

    Google Scholar 

  101. Wu, Z.: Commutative data automata. In: Proceedings of the 26th International Workshop, 21st Annual Conference on Computer Science Logic (CSL), pp. 528–542 (2012)

    Google Scholar 

  102. Wolper, P., Vardi, M.Y., Sistla, A.P.: Reasoning about infinite computation paths. In: Proceedings of the 24th Annual Symposium on Foundations of Computer Science (FOCS), pp. 185–194 (1983)

    Google Scholar 

  103. Zarba, C.G.: Combining sets with elements. In: Dershowitz, N. (ed.) Verification: Theory and Practice. LNCS, vol. 2772, pp. 762–782. Springer, Heidelberg (2003). doi:10.1007/978-3-540-39910-0_33

    Chapter  Google Scholar 

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Acknowledgments

Taolue Chen is partially supported by EPSRC grant (EP/P00430X/1), European CHIST-ERA project SUCCESS, ARC Discovery Project (DP160101652), Singapore MoE AcRF Tier 2 grant (MOE2015-T2-1-137), NSFC grant (No. 61662035), and an oversea grant from the State Key Laboratory of Novel Software Technology, Nanjing University (KFKT2014A14). Fu Song is partially supported by Shanghai Pujiang Program (No. 14PJ1403200), Shanghai ChenGuang Program (No. 13CG21), and NSFC Projects (Nos. 61402179, 61532019 and 91418203). Zhilin Wu is partially supported by the NSFC projects (Nos. 61100062, 61272135, 61472474, and 61572478).

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Authors and Affiliations

  1. Department of Computer Science, Middlesex University London, London, UK

    Taolue Chen

  2. School of Information Science and Technology, ShanghaiTech University, Shanghai, China

    Fu Song

  3. State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China

    Zhilin Wu

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  1. Taolue Chen
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  2. Fu Song
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  3. Zhilin Wu
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Correspondence to Zhilin Wu .

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  1. London South Bank University, London, United Kingdom

    Jonathan P. Bowen

  2. Southwest University, Chongqing, China

    Zhiming Liu

  3. Southwest University, Chongqing, China

    Zili Zhang

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Chen, T., Song, F., Wu, Z. (2017). Formal Reasoning on Infinite Data Values: An Ongoing Quest. In: Bowen, J., Liu, Z., Zhang, Z. (eds) Engineering Trustworthy Software Systems. SETSS 2016. Lecture Notes in Computer Science(), vol 10215. Springer, Cham. https://doi.org/10.1007/978-3-319-56841-6_6

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