Abstract
We present a tool that checks for a given context-free graph grammar whether the corresponding graph reduction system in which all rules are applied backward, is confluent—a question that arises when using graph grammars to guide state space abstractions for analyzing heap-manipulating programs; confluence of the graph reduction system then guarantees the abstraction’s uniqueness. If a graph reduction system is not confluent, our tool provides symbolic representations of counterexamples to confluence, i.e., non-joinable critical pairs, for manual inspection. Furthermore, it features a heuristics-based completion procedure that attempts to turn a graph reduction system into a confluent one without invalidating the properties mandated by the abstraction framework. We evaluate our implementation on various graph grammars for verifying data structure traversal algorithms from the literature.
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Notes
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That is, rules 2 and 3 were applied. To improve performance, Attestor generates specialized rules in which two or more external nodes are identical; the number after the dot indicates which case of a rule has been applied.
References
Arendt, T., Biermann, E., Jurack, S., Krause, C., Taentzer, G.: Henshin: advanced concepts and tools for in-place EMF model transformations. In: Petriu, D.C., Rouquette, N., Haugen, Ø. (eds.) MODELS 2010. LNCS, vol. 6394, pp. 121–135. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-16145-2_9
Arndt, H., Jansen, C., Katoen, J.-P., Matheja, C., Noll, T.: Let this graph be your witness!. In: Chockler, H., Weissenbacher, G. (eds.) CAV 2018. LNCS, vol. 10982, pp. 3–11. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96142-2_1
Arndt, H., Jansen, C., Matheja, C., Noll, T.: Graph-based shape analysis beyond context-freeness. In: Johnsen, E.B., Schaefer, I. (eds.) SEFM 2018. LNCS, vol. 10886, pp. 271–286. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-92970-5_17
Azzi, G.G., Bezerra, J.S., Ribeiro, L., Costa, A., Rodrigues, L.M., Machado, R.: The verigraph system for graph transformation. In: Heckel, R., Taentzer, G. (eds.) Graph Transformation, Specifications, and Nets. LNCS, vol. 10800, pp. 160–178. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-75396-6_9
Born, K., Arendt, T., Heß, F., Taentzer, G.: Analyzing conflicts and dependencies of rule-based transformations in Henshin. In: Egyed, A., Schaefer, I. (eds.) FASE 2015. LNCS, vol. 9033, pp. 165–168. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46675-9_11
Campbell, G., Plump, D.: Confluence up to garbage. In: Gadducci, F., Kehrer, T. (eds.) ICGT 2020. LNCS, vol. 12150, pp. 20–37. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-51372-6_2
Costa, A., et al.: Verigraph: a system for specification and analysis of graph grammars. In: Ribeiro, L., Lecomte, T. (eds.) SBMF 2016. LNCS, vol. 10090, pp. 78–94. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-49815-7_5
Deckwerth, F.: Static Verification Techniques for Attributed Graph Transformations. Ph.D. thesis, Technische Universität, Darmstadt (2017)
Drewes, F., Kreowski, H.J., Habel, A.: Hyperedge replacement graph grammars. In: Handbook of Graph Grammars and Computing by Graph Transformation, vol. I: Foundations, pp. 95–162. World Scientific (1997)
Fesefeldt, I.: moves-rwth/attestor-confluence. https://github.com/moves-rwth/attestor-confluence/blob/master/readme/HEURISTICS.md
Heckel, R., Küster, J.M., Taentzer, G.: Confluence of typed attributed graph transformation systems. In: Corradini, A., Ehrig, H., Kreowski, H.-J., Rozenberg, G. (eds.) ICGT 2002. LNCS, vol. 2505, pp. 161–176. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45832-8_14
Heinen, J., Jansen, C., Katoen, J.P., Noll, T.: Verifying pointer programs using graph grammars. Sci. Comput. Programm. 97(1), 157–162 (2015)
Hoffmann, B., Plump, D.: Implementing term rewriting by jungle evaluation. RAIRO Theor. Inform. Appl. 25, 445–472 (1991)
Hristakiev, I., Plump, D.: Checking graph programs for confluence. In: Seidl, M., Zschaler, S. (eds.) STAF 2017. LNCS, vol. 10748, pp. 92–108. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-74730-9_8
Jansen, C.: Static Analysis of Pointer Programs - Linking Graph Grammars and Separation Logic. Ph.D. thesis, RWTH Aachen University, Germany (2017)
Jansen, C., Heinen, J., Katoen, J.-P., Noll, T.: A local greibach normal form for hyperedge replacement grammars. In: Dediu, A.-H., Inenaga, S., Martín-Vide, C. (eds.) LATA 2011. LNCS, vol. 6638, pp. 323–335. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-21254-3_25
Knuth, D., Bendix, P.: Simple word problems in universal algebra. Computational Problems in Abstract Algebra, pp. 263–297 (1970)
Lambers, L., Born, K., Kosiol, J., Strüber, D., Taentzer, G.: Granularity of conflicts and dependencies in graph transformation systems: a two-dimensional approach. J. Logic. Algebraic Meth. Program. 103, 105–129 (2019)
Lambers, L., Ehrig, H., Orejas, F.: Conflict detection for graph transformation with negative application conditions. In: Corradini, A., Ehrig, H., Montanari, U., Ribeiro, L., Rozenberg, G. (eds.) ICGT 2006. LNCS, vol. 4178, pp. 61–76. Springer, Heidelberg (2006). https://doi.org/10.1007/11841883_6
Lambers, L., Ehrig, H., Orejas, F.: Efficient conflict detection in graph transformation systems by essential critical pairs. Electron. Notes Theor. Comput. Sci. 211, 17–26 (2008)
Matheja, C.: Automated reasoning and randomization in separation logic. Ph.D. thesis, RWTH Aachen University, Germany (2020)
Matheja, C., Jansen, C., Noll, T.: Tree-like grammars and separation logic. In: Feng, X., Park, S. (eds.) APLAS 2015. LNCS, vol. 9458, pp. 90–108. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-26529-2_6
Plump, D.: Confluence of graph transformation revisited. In: Middeldorp, A., van Oostrom, V., van Raamsdonk, F., de Vrijer, R. (eds.) Processes, Terms and Cycles: Steps on the Road to Infinity. LNCS, vol. 3838, pp. 280–308. Springer, Heidelberg (2005). https://doi.org/10.1007/11601548_16
Plump, D.: Checking graph-transformation systems for confluence. ECEASST 26 (2010)
Runge, O., Ermel, C., Taentzer, G.: AGG 2.0 – new features for specifying and analyzing algebraic graph transformations. In: Schürr, A., Varró, D., Varró, G. (eds.) AGTIVE 2011. LNCS, vol. 7233, pp. 81–88. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-34176-2_8
Schulte, J.: Automated Detection and Completion of Confluence for Graph Grammars. Master thesis, RWTH Aachen University, Germany (2019). http://www-i2.informatik.rwth-aachen.de/pub/index.php?type=download&pub_id=1765
Taentzer, G.: AGG: a graph transformation environment for modeling and validation of software. In: Pfaltz, J.L., Nagl, M., Böhlen, B. (eds.) AGTIVE 2003. LNCS, vol. 3062, pp. 446–453. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-25959-6_35
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Fesefeldt, I., Matheja, C., Noll, T., Schulte, J. (2021). Automated Checking and Completion of Backward Confluence for Hyperedge Replacement Grammars. In: Gadducci, F., Kehrer, T. (eds) Graph Transformation. ICGT 2021. Lecture Notes in Computer Science(), vol 12741. Springer, Cham. https://doi.org/10.1007/978-3-030-78946-6_15
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