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Synthesis from Weighted Specifications with Partial Domains over Finite Words

Authors Emmanuel Filiot, Christof Löding, Sarah Winter

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Emmanuel Filiot
  • Université libre de Bruxelles, Belgium
Christof Löding
  • RWTH Aachen University, Germany
Sarah Winter
  • Université libre de Bruxelles, Belgium

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Emmanuel Filiot, Christof Löding, and Sarah Winter. Synthesis from Weighted Specifications with Partial Domains over Finite Words. In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, pp. 46:1-46:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


In this paper, we investigate the synthesis problem of terminating reactive systems from quantitative specifications. Such systems are modeled as finite transducers whose executions are represented as finite words in (I × O)^*, where I, O are finite sets of input and output symbols, respectively. A weighted specification S assigns a rational value (or -∞) to words in (I × O)^*, and we consider three kinds of objectives for synthesis, namely threshold objectives where the system’s executions are required to be above some given threshold, best-value and approximate objectives where the system is required to perform as best as it can by providing output symbols that yield the best value and ε-best value respectively w.r.t. S. We establish a landscape of decidability results for these three objectives and weighted specifications with partial domain over finite words given by deterministic weighted automata equipped with sum, discounted-sum and average measures. The resulting objectives are not regular in general and we develop an infinite game framework to solve the corresponding synthesis problems, namely the class of (weighted) critical prefix games.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and verification
  • Theory of computation → Transducers
  • Theory of computation → Quantitative automata
  • synthesis
  • weighted games
  • weighted automata on finite words


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