On the specification of operations on the rational behaviour of systems

Structural operational semantics can be studied at the general level of distributive laws of syntax over behaviour. This yields specification formats for well-behaved algebraic operations on final coalgebras, which are a domain for the behaviour of all systems of a given type functor. We introduce a format for specification of algebraic operations that restrict to the rational fixpoint of a functor, which captures the behaviour of finite systems. In other words, we show that rational behaviour is closed under operations specified in our format. As applications we consider operations on regular languages, regular processes and finite weighted transition systems.

[1]  Susanna Ginali,et al.  Regular Trees and the Free Iterative Theory , 1979, J. Comput. Syst. Sci..

[2]  F. Bartels,et al.  On Generalised Coinduction and Probabilistic Specification Formats , 2004 .

[4]  Alexandra Silva,et al.  Sound and Complete Axiomatizations of Coalgebraic Language Equivalence , 2011, TOCL.

[5]  Jirí Adámek,et al.  Iterative algebras at work , 2006, Mathematical Structures in Computer Science.

[6]  Gordon D. Plotkin,et al.  Towards a mathematical operational semantics , 1997, Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science.

[7]  Bruno Courcelle,et al.  Fundamental Properties of Infinite Trees , 1983, Theor. Comput. Sci..

[8]  Bartek Klin,et al.  Bialgebras for structural operational semantics: An introduction , 2011, Theor. Comput. Sci..

[9]  Jan J. M. M. Rutten,et al.  A coinductive calculus of streams , 2005, Mathematical Structures in Computer Science.

[10]  Robin Milner,et al.  Communication and concurrency , 1989, PHI Series in computer science.

[11]  James Worrell,et al.  On the final sequence of a finitary set functor , 2005, Theor. Comput. Sci..

[12]  Jeffrey Shallit,et al.  A Second Course in Formal Languages and Automata Theory , 2008 .

[13]  Jirí Adámek,et al.  Free iterative theories: a coalgebraic view , 2003, Mathematical Structures in Computer Science.

[14]  Luca Aceto,et al.  Structural Operational Semantics , 1999, Handbook of Process Algebra.

[15]  P. Gabriel,et al.  Lokal α-präsentierbare Kategorien , 1971 .

[16]  Luca Aceto,et al.  GSOS and Finite Labelled Transition Systems , 1994, Theor. Comput. Sci..

[17]  Bartek Klin,et al.  Bialgebraic Operational Semantics and Modal Logic , 2007, 22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007).

[18]  Michael Makkai,et al.  Accessible categories: The foundations of categorical model theory, , 2007 .

[19]  J. Adámek,et al.  Locally presentable and accessible categories , 1994 .

[20]  M. Droste,et al.  Handbook of Weighted Automata , 2009 .

[21]  Bartek Klin,et al.  Structural Operational Semantics for Weighted Transition Systems , 2009, Semantics and Algebraic Specification.

[22]  J. Lambek.  A fixpoint theorem for complete categories , 1968 .

[23]  J. Adámek,et al.  Automata and Algebras in Categories , 1990 .

[24]  Michael Barr,et al.  Terminal Coalgebras in Well-Founded Set Theory , 1993, Theor. Comput. Sci..

[25]  Albert R. Meyer,et al.  Bisimulation can't be traced , 1988, POPL '88.

[26]  Stefan Milius.  A Sound and Complete Calculus for Finite Stream Circuits , 2010, 2010 25th Annual IEEE Symposium on Logic in Computer Science.

[27]  Jan J. M. M. Rutten.  Rational Streams Coalgebraically , 2008, Log. Methods Comput. Sci..