Coalgebraic Logic and Synthesis of Mealy Machines

We present a novel coalgebraic logic for deterministic Mealy machines that is sound, complete and expressive w.r.t. bisimulation. Every finite Mealy machine corresponds to a finite formula in the language. For the converse, we give a compositional synthesis algorithm which transforms every formula into a finite Mealy machine whose behaviour is exactly the set of causal functions satisfying the formula.

[1]  Amir Pnueli,et al.  On the synthesis of a reactive module , 1989, POPL '89.

[2]  Nicoletta Sabadini,et al.  Feedback, trace and fixed-point semantics , 2002, RAIRO Theor. Informatics Appl..

[3]  Dexter Kozen,et al.  Results on the Propositional µ-Calculus , 1982, ICALP.

[4]  Jan J. M. M. Rutten,et al.  Synthesis of Mealy Machines Using Derivatives , 2006, CMCS.

[5]  Andrea Maggiolo-Schettini,et al.  Compositional Synthesis of Generalized Mealy Machines , 2004, Fundam. Informaticae.

[6]  Lawrence S. Moss,et al.  Coalgebraic Logic , 1999, Ann. Pure Appl. Log..

[7]  Yde Venema,et al.  Coalgebraic Automata Theory: Basic Results , 2008, Log. Methods Comput. Sci..

[8]  Alan Marcovitz.  Introduction to Logic Design with CD ROM , 2004 .

[9]  Orna Kupferman,et al.  µ-Calculus Synthesis , 2000, MFCS.

[10]  Sajjan G. Shiva,et al.  Introduction to Logic Design , 2018 .

[11]  Pierre Wolper,et al.  An automata-theoretic approach to branching-time model checking , 2000, JACM.

[12]  Helmut Veith,et al.  Executable Protocol Specification in ESL , 2000, FMCAD.

[13]  M. M. Bonsangue,et al.  Software ENgineering Coalgebraic logic and synthesis of Mealy machines , 2007 .

[14]  Marcello M. Bonsangue,et al.  Presenting Functors by Operations and Equations, in Foundations of Software Science and Computation Structures , 2006, SIGMETRICS 2006.

[15]  Marcello M. Bonsangue,et al.  Duality for Logics of Transition Systems , 2005, FoSSaCS.

[16]  Marcello M. Bonsangue,et al.  Presenting Functors by Operations and Equations , 2006, FoSSaCS.

[17]  S. Shelah,et al.  Annals of Pure and Applied Logic , 1991 .

[18]  Jan J. M. M. Rutten,et al.  Algebraic Specification and Coalgebraic Synthesis of Mealy Automata , 2006, FACS.