Automata and Coinduction (An Exercise in Coalgebra)

The classical theory of deterministic automata is presented in terms of the notions of homomorphism and bisimulation, which are the cornerstones of the theory of (universal) coalgebra. This leads to a transparent and uniform presentation of automata theory and yields some new insights, amongst which coinduction proof methods for language equality and language inclusion. At the same time, the present treatment of automata theory may serve as an introduction to coalgebra.

[1]  A. Nerode,et al.  Linear automaton transformations , 1958 .

[2]  Peter Aczel,et al.  A Final Coalgebra Theorem , 1989, Category Theory and Computer Science.

[3]  Lawrence S. Moss,et al.  Vicious circles - on the mathematics of non-wellfounded phenomena , 1996, CSLI lecture notes series.

[4]  J. W. de Bakker,et al.  Comparative Semantics for Flow of Control in Logic Programming without Logic , 1991, Inf. Comput..

[5]  Jan J. M. M. Rutten,et al.  On the Foundation of Final Semantics: Non-Standard Sets, Metric Spaces, Partial Orders , 1992, REX Workshop.

[6]  M. Dal Cin,et al.  The Algebraic Theory of Automata , 1980 .

[7]  Abraham Ginzburg,et al.  Chapter 5 – Coverings of Automata , 1968 .

[8]  Gérard Berry,et al.  From Regular Expressions to Deterministic Automata , 1986, Theor. Comput. Sci..

[9]  Janusz A. Brzozowski,et al.  Derivatives of Regular Expressions , 1964, JACM.

[10]  Dana S. Scott,et al.  Finite Automata and Their Decision Problems , 1959, IBM J. Res. Dev..

[11]  C. Pollard,et al.  Center for the Study of Language and Information , 2022 .

[12]  Ferenc Gécseg,et al.  Products of Automata , 1986, EATCS Monographs in Theoretical Computer Science.

[13]  Dexter Kozen.  A Completeness Theorem for Kleene Algebras and the Algebra of Regular Events , 1994, Inf. Comput..

[14]  B. Jacobs,et al.  A tutorial on (co)algebras and (co)induction , 1997 .

[15]  J. Conway.  Regular algebra and finite machines , 1971 .

[16]  S C Kleene,et al.  Representation of Events in Nerve Nets and Finite Automata , 1951 .

[17]  Arto Salomaa,et al.  Two Complete Axiom Systems for the Algebra of Regular Events , 1966, JACM.

[18]  Robin Milner,et al.  A Calculus of Communicating Systems , 1980, Lecture Notes in Computer Science.

[19]  Chrysa s Hartonas,et al.  Duality for Modal mu-Logics , 1998, Theor. Comput. Sci..

[20]  Jan J. M. M. Rutten,et al.  Universal coalgebra: a theory of systems , 2000, Theor. Comput. Sci..

[21]  Franck van Breugel,et al.  Terminal Metric Spaces of Finitely Branching and Image Finite Linear Processes , 1998, Theor. Comput. Sci..

[22]  Bart Jacobs,et al.  Preface: Volume 11 , 1998 .

[23]  David Park,et al.  Concurrency and Automata on Infinite Sequences , 1981, Theoretical Computer Science.