{"oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"text":"The traditional synthesis question given a specification asks for the automatic construction of a system that satisfies the specification, whereas often there exists a preference order among the different systems that satisfy the given specification. Under a probabilistic assumption about the possible inputs, such a preference order is naturally expressed by a weighted automaton, which assigns to each word a value, such that a system is preferred if it generates a higher expected value. We solve the following optimal synthesis problem: given an omega-regular specification, a Markov chain that describes the distribution of inputs, and a weighted automaton that measures how well a system satisfies the given specification under the input assumption, synthesize a system that optimizes the measured value. For safety specifications and quantitative measures that are defined by mean-payoff automata, the optimal synthesis problem reduces to finding a strategy in a Markov decision process (MDP) that is optimal for a long-run average reward objective, which can be achieved in polynomial time. For general omega-regular specifications along with mean-payoff automata, the solution rests on a new, polynomial-time algorithm for computing optimal strategies in MDPs with mean-payoff parity objectives. Our algorithm constructs optimal strategies that consist of two memoryless strategies and a counter. The counter is in general not bounded. To obtain a finite-state system, we show how to construct an ε-optimal strategy with a bounded counter, for all ε &gt; 0. Furthermore, we show how to decide in polynomial time if it is possible to construct an optimal finite-state system (i.e., a system without a counter) for a given specification. We have implemented our approach and the underlying algorithms in a tool that takes qualitative and quantitative specifications and automatically constructs a system that satisfies the qualitative specification and optimizes the quantitative specification, if such a system exists. We present some experimental results showing optimal systems that were automatically generated in this way.","lang":"eng"}],"publisher":"ACM","oa":1,"day":"01","date_updated":"2023-02-23T11:46:04Z","language":[{"iso":"eng"}],"year":"2015","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1004.0739"}],"intvolume":"        62","publist_id":"5244","publication":"Journal of the ACM","ec_funded":1,"doi":"10.1145/2699430","project":[{"name":"Quantitative Reactive Modeling","call_identifier":"FP7","grant_number":"267989","_id":"25EE3708-B435-11E9-9278-68D0E5697425"},{"name":"Rigorous Systems Engineering","grant_number":"S 11407_N23","call_identifier":"FWF","_id":"25832EC2-B435-11E9-9278-68D0E5697425"},{"grant_number":"P 23499-N23","call_identifier":"FWF","name":"Modern Graph Algorithmic Techniques in Formal Verification","_id":"2584A770-B435-11E9-9278-68D0E5697425"},{"_id":"25863FF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"S11407","name":"Game Theory"},{"call_identifier":"FP7","grant_number":"279307","name":"Quantitative Graph Games: Theory and Applications","_id":"2581B60A-B435-11E9-9278-68D0E5697425"},{"name":"Microsoft Research Faculty Fellowship","_id":"2587B514-B435-11E9-9278-68D0E5697425"}],"title":"Measuring and synthesizing systems in probabilistic environments","date_published":"2015-02-01T00:00:00Z","date_created":"2018-12-11T11:54:23Z","scopus_import":1,"related_material":{"record":[{"id":"3864","status":"public","relation":"earlier_version"}]},"article_number":"9","author":[{"id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","first_name":"Krishnendu","last_name":"Chatterjee","orcid":"0000-0002-4561-241X","full_name":"Chatterjee, Krishnendu"},{"id":"40876CD8-F248-11E8-B48F-1D18A9856A87","last_name":"Henzinger","first_name":"Thomas A","orcid":"0000−0002−2985−7724","full_name":"Henzinger, Thomas A"},{"first_name":"Barbara","last_name":"Jobstmann","full_name":"Jobstmann, Barbara"},{"full_name":"Singh, Rohit","first_name":"Rohit","last_name":"Singh"}],"month":"02","citation":{"short":"K. Chatterjee, T.A. Henzinger, B. Jobstmann, R. Singh, Journal of the ACM 62 (2015).","ieee":"K. Chatterjee, T. A. Henzinger, B. Jobstmann, and R. Singh, “Measuring and synthesizing systems in probabilistic environments,” <i>Journal of the ACM</i>, vol. 62, no. 1. ACM, 2015.","ista":"Chatterjee K, Henzinger TA, Jobstmann B, Singh R. 2015. Measuring and synthesizing systems in probabilistic environments. Journal of the ACM. 62(1), 9.","mla":"Chatterjee, Krishnendu, et al. “Measuring and Synthesizing Systems in Probabilistic Environments.” <i>Journal of the ACM</i>, vol. 62, no. 1, 9, ACM, 2015, doi:<a href=\"https://doi.org/10.1145/2699430\">10.1145/2699430</a>.","apa":"Chatterjee, K., Henzinger, T. A., Jobstmann, B., &#38; Singh, R. (2015). Measuring and synthesizing systems in probabilistic environments. <i>Journal of the ACM</i>. ACM. <a href=\"https://doi.org/10.1145/2699430\">https://doi.org/10.1145/2699430</a>","chicago":"Chatterjee, Krishnendu, Thomas A Henzinger, Barbara Jobstmann, and Rohit Singh. “Measuring and Synthesizing Systems in Probabilistic Environments.” <i>Journal of the ACM</i>. ACM, 2015. <a href=\"https://doi.org/10.1145/2699430\">https://doi.org/10.1145/2699430</a>.","ama":"Chatterjee K, Henzinger TA, Jobstmann B, Singh R. Measuring and synthesizing systems in probabilistic environments. <i>Journal of the ACM</i>. 2015;62(1). doi:<a href=\"https://doi.org/10.1145/2699430\">10.1145/2699430</a>"},"status":"public","_id":"1856","volume":62,"publication_status":"published","quality_controlled":"1","department":[{"_id":"KrCh"},{"_id":"ToHe"}],"issue":"1","type":"journal_article"}