Model Repair Revamped: On the Automated Synthesis of Markov Chains

This paper outlines two approaches—based on counterexampleguided abstraction refinement (CEGAR) and counterexample-guided inductive synthesis (CEGIS), respectively—to the automated synthesis of finite-state probabilistic models and programs. Our CEGAR approach iteratively partitions the design space starting from an abstraction of this space and refines this by a light-weight analysis of verification results. The CEGIS technique exploits critical subsystems as counterexamples to prune all programs behaving incorrectly on that input. We show the applicability of these synthesis techniques to sketching of probabilistic programs, controller synthesis of POMDPs, and software product lines.

[1]  Christel Baier,et al.  ProFeat: feature-oriented engineering for family-based probabilistic model checking , 2017, Formal Aspects of Computing.

[2]  Ventsislav Chonev,et al.  Reachability in Augmented Interval Markov Chains , 2017, RP.

[3]  C. R. Ramakrishnan,et al.  Model Repair for Probabilistic Systems , 2011, TACAS.

[4]  Annabelle McIver,et al.  Probabilistic predicate transformers , 1996, TOPL.

[5]  Sebastian Junges,et al.  Synthesis in pMDPs: A Tale of 1001 Parameters , 2018, ATVA.

[6]  Nils Jansen,et al.  Minimal counterexamples for linear-time probabilistic verification , 2014, Theor. Comput. Sci..

[7]  Armando Solar-Lezama,et al.  Program sketching , 2012, International Journal on Software Tools for Technology Transfer.

[8]  Nils Jansen,et al.  Fast Debugging of PRISM Models , 2014, ATVA.

[9]  Scott A. Smolka,et al.  Abstract Model Repair , 2012, NASA Formal Methods.

[10]  Armando Solar-Lezama,et al.  Programming by sketching for bit-streaming programs , 2005, PLDI '05.

[11]  David Barber,et al.  On the Computational Complexity of Stochastic Controller Optimization in POMDPs , 2011, TOCT.

[12]  Adnan Aziz,et al.  It Usually Works: The Temporal Logic of Stochastic Systems , 1995, CAV.

[13]  Sebastian Junges,et al.  Permissive Finite-State Controllers of POMDPs using Parameter Synthesis , 2017, ArXiv.

[14]  Edmund M. Clarke,et al.  Counterexample-guided abstraction refinement , 2003, 10th International Symposium on Temporal Representation and Reasoning, 2003 and Fourth International Conference on Temporal Logic. Proceedings..

[15]  Sebastian Junges,et al.  Shepherding Hordes of Markov Chains , 2019, TACAS.

[16]  Pierre-Yves Schobbens,et al.  Modeling and Verification for Probabilistic Properties in Software Product Lines , 2015, 2015 IEEE 16th International Symposium on High Assurance Systems Engineering.

[17]  Sebastian Junges,et al.  Counterexample-Driven Synthesis for Probabilistic Program Sketches , 2019, FM.

[18]  Pierre-Yves Schobbens,et al.  Model checking software product lines with SNIP , 2012, International Journal on Software Tools for Technology Transfer.

[19]  Sriram K. Rajamani,et al.  Efficient synthesis of probabilistic programs , 2015, PLDI.

[20]  Sebastian Junges,et al.  JANI: Quantitative Model and Tool Interaction , 2017, TACAS.

[21]  Christel Baier,et al.  Principles of model checking , 2008 .

[22]  Leslie Pack Kaelbling,et al.  Planning and Acting in Partially Observable Stochastic Domains , 1998, Artif. Intell..

[23]  Krishnendu Chatterjee,et al.  What is decidable about partially observable Markov decision processes with ω-regular objectives , 2013, J. Comput. Syst. Sci..

[24]  Jun Sun,et al.  Learning probabilistic models for model checking: an evolutionary approach and an empirical study , 2018, International Journal on Software Tools for Technology Transfer.

[25]  Rajeev Alur,et al.  Search-based program synthesis , 2018, Commun. ACM.

[26]  Georg Gottlob,et al.  Enhancing Model Checking in Verification by AI Techniques , 1999, Artif. Intell..

[27]  Sebastian Junges,et al.  PROPhESY: A PRObabilistic ParamEter SYnthesis Tool , 2015, CAV.

[28]  Krishnendu Chatterjee,et al.  A Symbolic SAT-Based Algorithm for Almost-Sure Reachability with Small Strategies in POMDPs , 2015, AAAI.

[29]  Sarah E. Chasins,et al.  Data-Driven Synthesis of Full Probabilistic Programs , 2017, CAV.

[30]  Joost-Pieter Katoen,et al.  The Probabilistic Model Checking Landscape* , 2016, 2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS).

[31]  Lijun Zhang,et al.  Model Repair for Markov Decision Processes , 2013, 2013 International Symposium on Theoretical Aspects of Software Engineering.

[32]  Marta Z. Kwiatkowska,et al.  PRISM 4.0: Verification of Probabilistic Real-Time Systems , 2011, CAV.

[33]  Holger Hermanns,et al.  MODEST: A Compositional Modeling Formalism for Hard and Softly Timed Systems , 2006, IEEE Transactions on Software Engineering.

[34]  Radu Calinescu,et al.  Search-Based Synthesis of Probabilistic Models for Quality-of-Service Software Engineering (T) , 2015, 2015 30th IEEE/ACM International Conference on Automated Software Engineering (ASE).

[35]  C. Cordell Green,et al.  What Is Program Synthesis? , 1985, J. Autom. Reason..

[36]  Kee-Eung Kim,et al.  Solving POMDPs by Searching the Space of Finite Policies , 1999, UAI.

[37]  Scott A. Smolka,et al.  Composition and Behaviors of Probabilistic I/O Automata , 1994, Theor. Comput. Sci..

[38]  Stanisa Dautovic,et al.  Dynamic Power Management of a System With a Two-Priority Request Queue Using Probabilistic-Model Checking , 2008, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[39]  Luca Benini,et al.  Policy optimization for dynamic power management , 1998, Proceedings 1998 Design and Automation Conference. 35th DAC. (Cat. No.98CH36175).

[40]  Nils Jansen,et al.  A Greedy Approach for the Efficient Repair of Stochastic Models , 2015, NFM.

[41]  Christel Baier,et al.  Model Checking Probabilistic Systems , 2018, Handbook of Model Checking.

[42]  Kim G. Larsen,et al.  Learning deterministic probabilistic automata from a model checking perspective , 2016, Machine Learning.