Compositional Algorithms for Succinct Safety Games

We study the synthesis of circuits for succinct safety specifications given in the AIG format. We show how AIG safety specifications can be decomposed automatically into sub-specifications. Then we propose symbolic compositional algorithms to solve the synthesis problem compositionally starting for the sub-specifications. We have evaluated the compositional algorithms on a set of benchmarks including those proposed for the first synthesis competition organised in 2014 by the Synthesis Workshop affiliated to the CAV conference. We show that a large number of benchmarks can be decomposed automatically and solved more efficiently with the compositional algorithms that we propose in this paper.

[1]  E. Allen Emerson,et al.  Tree automata, mu-calculus and determinacy , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.

[2]  Jean-François Raskin,et al.  Compositional Algorithms for LTL Synthesis , 2010, ATVA.

[3]  Krzysztof R. Apt,et al.  Lectures in Game Theory for Computer Scientists , 2011 .

[4]  Guillermo A. Pérez,et al.  AbsSynthe: abstract synthesis from succinct safety specifications , 2014, SYNT.

[5]  F. Somenzi Binary Decision Diagrams , 1999 .

[6]  Robert K. Brayton,et al.  Heuristic Minimization of BDDs Using Don't Cares , 1994, 31st Design Automation Conference.

[7]  Robert K. Brayton,et al.  Implicit state enumeration of finite state machines using BDD's , 1990, 1990 IEEE International Conference on Computer-Aided Design. Digest of Technical Papers.

[8]  Chao Wang,et al.  The compositional far side of image computation , 2003, ICCAD-2003. International Conference on Computer Aided Design (IEEE Cat. No.03CH37486).

[9]  Jean-François Raskin,et al.  Antichains and compositional algorithms for LTL synthesis , 2011, Formal Methods Syst. Des..

[10]  H. Andersen An Introduction to Binary Decision Diagrams , 1997 .

[11]  E BryantRandal Graph-Based Algorithms for Boolean Function Manipulation , 1986 .

[12]  Sheldon B. Akers,et al.  Binary Decision Diagrams , 1978, IEEE Transactions on Computers.

[13]  Edmund M. Clarke,et al.  Symbolic Model Checking with Partitioned Transistion Relations , 1991, VLSI.

[14]  Edmund M. Clarke,et al.  Model Checking , 1999, Handbook of Automated Reasoning.

[15]  A. Tarski A LATTICE-THEORETICAL FIXPOINT THEOREM AND ITS APPLICATIONS , 1955 .

[16]  Amir Pnueli,et al.  Synthesis of Reactive(1) designs , 2006, J. Comput. Syst. Sci..