On Nominal Regular Languages with Binders

We investigate regular languages on infinite alphabets where words may contain binders on names. To this end, classical regular expressions and automata are extended with binders. We prove the equivalence between finite automata on binders and regular expressions with binders and investigate closure properties and complementation of regular languages with binders.

[1]  Emilio Tuosto,et al.  Towards Nominal Formal Languages , 2011, ArXiv.

[2]  Maribel Fernández,et al.  Nominal rewriting , 2007, Inf. Comput..

[3]  Alex K. Simpson,et al.  Computational Adequacy in an Elementary Topos , 1998, CSL.

[4]  Colin Stirling,et al.  Dependency Tree Automata , 2009, FoSSaCS.

[5]  Andrew M. Pitts,et al.  Observable Properties of Higher Order Functions that Dynamically Create Local Names, or What's new? , 1993, MFCS.

[6]  Sam Staton,et al.  Comparing Operational Models of Name-Passing Process Calculi , 2004, CMCS.

[7]  Marco Pistore,et al.  π-Calculus, structured coalgebras, and minimal HD-automata , 2000 .

[8]  Andrew M. Pitts,et al.  FreshML: programming with binders made simple , 2003, ICFP '03.

[9]  Fabio Gadducci,et al.  About permutation algebras, (pre)sheaves and named sets , 2006, High. Order Symb. Comput..

[10]  M. Arbib,et al.  MACHINES IN A CATEGORY: AN EXPOSITORY INTRODUCTION* , 1974 .

[11]  Nikos Tzevelekos.  Fresh-register automata , 2011, POPL '11.

[12]  Robin Milner.  Action Calculi, or Syntactic Action Structures , 1993, MFCS.

[13]  M. Stone,et al.  Postulates for Boolean Algebras and Generalized Boolean Algebras , 1935 .

[14]  Luc Segoufin.  Automata and Logics for Words and Trees over an Infinite Alphabet , 2006, CSL.

[15]  Nissim Francez,et al.  Finite-Memory Automata , 1994, Theor. Comput. Sci..

[16]  Mikolaj Bojanczyk.  Data Monoids , 2011, STACS.

[17]  R. Alur,et al.  Adding nesting structure to words , 2006, JACM.

[18]  Gottfried Vossen,et al.  Transactional Information Systems: Theory, Algorithms, and the Practice of Concurrency Control and Recovery , 2002 .

[19]  Mogens Nielsen,et al.  Mathematical Foundations of Computer Science 2000 , 2001, Lecture Notes in Computer Science.

[20]  Ugo Montanari,et al.  History-Dependent Automata , 1998 .

[21]  Gerhard Weikum,et al.  CHAPTER FOUR – Concurrency Control Algorithms , 2002 .

[22]  François Pottier,et al.  A fresh look at programming with names and binders , 2010, ICFP '10.

[23]  Marc H. Scholl,et al.  Transactional information systems: theory, algorithms, and the practice of concurrency control and recovery , 2001, SGMD.

[24]  Vincenzo Ciancia,et al.  Symmetries, local names and dynamic (de)-allocation of names , 2010, Inf. Comput..

[25]  Ian Stark,et al.  Free-Algebra Models for the pi-Calculus , 2005, FoSSaCS.

[26]  Vincenzo Ciancia,et al.  Freshness and Name-Restriction in Sets of Traces with Names , 2011, FoSSaCS.

[27]  Andrew M. Pitts,et al.  A new approach to abstract syntax involving binders , 1999, Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158).

[28]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[29]  Marco Pistore,et al.  pi-Calculus, Structured Coalgebras, and Minimal HD-Automata , 2000, MFCS.

[30]  Joost Engelfriet,et al.  Tree-Walking Pebble Automata , 1999, Jewels are Forever.

[31]  Dexter Kozen,et al.  Local variable scoping and Kleene algebra with tests , 2008, J. Log. Algebraic Methods Program..

[32]  Slawomir Lasota,et al.  Automata with Group Actions , 2011, 2011 IEEE 26th Annual Symposium on Logic in Computer Science.