The expressivity of universal timed CCP: undecidability of Monadic FLTL and closure operators for security

The timed concurrent constraint programing model (tcc) is a declarative framework, closely related to First-Order Linear Temporal Logic (FLTL), for modeling reactive systems. The universal tcc formalism (utcc) is an extension of tcc with the ability to express mobility. Here mobility is understood as communication of private names as typically done for mobile systems and security protocols. This paper is devoted to the study of 1) the expressiveness of utcc and 2) its semantic foundations. As applications of this study, we also state 3) a noteworthy decidability result for the wellestablished framework of FLTL and 4) bring new semantic insights into the modeling of security protocols. More precisely, we show that in contrast to tcc, utcc is Turingpowerful by encoding Minsky machines. The encoding uses a monadic constraint system allowing us to prove a new result for a fragment of FLTL: The undecidability of the validity problem for monadic FLTL without equality and function symbols. This result refutes a decidability conjecture for FLTL from a previous paper. It also justifies the restriction imposed in previous decidability results on the quantification of flexible-variables. We shall also show that as in tcc, utcc processes can be semantically represented as partial closure operators. The representation is fully abstract wrt the input-output behavior of processes for a meaningful fragment of the utcc. This shows that mobility can be captured as closure operators over an underlying constraint system. As an application we identify a language for security protocols that can be represented as closure operators over a cryptographic constraint system.

[1]  Andrzej Szalas,et al.  Incompleteness of First-Order Temporal Logic with Until , 1988, Theor. Comput. Sci..

[2]  Martín Abadi,et al.  Analyzing security protocols with secrecy types and logic programs , 2002, POPL '02.

[3]  Vijay A. Saraswat,et al.  Concurrent constraint programming , 1989, POPL '90.

[4]  Robin Milner,et al.  Communicating and mobile systems - the Pi-calculus , 1999 .

[5]  Maria Grazia Buscemi,et al.  A method for symbolic analysis of security protocols , 2005, Theor. Comput. Sci..

[6]  Martín Abadi,et al.  Computing symbolic models for verifying cryptographic protocols , 2001, Proceedings. 14th IEEE Computer Security Foundations Workshop, 2001..

[7]  Frank Wolter,et al.  Decidable fragment of first-order temporal logics , 2000, Ann. Pure Appl. Log..

[8]  Frank D. Valencia,et al.  Decidability of infinite-state timed CCP processes and first-order LTL , 2005, Theor. Comput. Sci..

[9]  Zohar Manna,et al.  The Temporal Logic of Reactive and Concurrent Systems , 1991, Springer New York.

[10]  R. McNaughton.  Review: J. Richard Buchi, Weak Second-Order Arithmetic and Finite Automata; J. Richard Buchi, On a Decision Method in Restricted second Order Arithmetic , 1963, Journal of Symbolic Logic.

[11]  Maurizio Gabbrielli,et al.  Proving concurrent constraint programs correct , 1997, TOPL.

[12]  Martín Abadi,et al.  Corrigendum: The Power of Temporal Proofs , 1990, Theor. Comput. Sci..

[13]  S. Sieber.  On a decision method in restricted second-order arithmetic , 1960 .

[14]  Prakash Panangaden,et al.  The semantic foundations of concurrent constraint programming , 1991, POPL '91.

[15]  Bruno Blanchet.  Security protocols: from linear to classical logic by abstract interpretation , 2005, Inf. Process. Lett..

[16]  Stephan Merz,et al.  Decidability and incompleteness results for first-order temporal logics of linear time , 1992, J. Appl. Non Class. Logics.

[17]  Yuri Gurevich,et al.  The Classical Decision Problem , 1997, Perspectives in Mathematical Logic.

[18]  Giovanni Maria Sacco,et al.  Timestamps in key distribution protocols , 1981, CACM.

[19]  Roberto M. Amadio,et al.  On the symbolic reduction of processes with cryptographic functions , 2003, Theor. Comput. Sci..

[20]  Frank D. Valencia,et al.  Temporal Concurrent Constraint Programming: Denotation, Logic and Applications , 2002, Nord. J. Comput..

[21]  Martín Abadi,et al.  The power of temporal proofs (corrigendum) , 1990 .

[22]  Martín Abadi,et al.  A calculus for cryptographic protocols: the spi calculus , 1997, CCS '97.

[23]  Agostino Cortesi,et al.  Complementation in abstract interpretation , 1997, TOPL.

[24]  Martín Abadi,et al.  Hiding Names: Private Authentication in the Applied Pi Calculus , 2002, ISSS.

[25]  Frank D. Valencia,et al.  On the expressive power of temporal concurrent constraint programming languages , 2002, PPDP '02.

[26]  Frank D. Valencia,et al.  Universal concurrent constraint programing: symbolic semantics and applications to security , 2008, SAC '08.

[27]  Michael Fisher,et al.  Equality and Monodic First-Order Temporal Logic , 2002, Stud Logica.

[28]  Radha Jagadeesan,et al.  Foundations of timed concurrent constraint programming , 1994, Proceedings Ninth Annual IEEE Symposium on Logic in Computer Science.

[29]  Glynn Winskel,et al.  Petri nets in cryptographic protocols , 2001, Proceedings 15th International Parallel and Distributed Processing Symposium. IPDPS 2001.