Separating Fairness and Well-Foundedness for the Analysis of Fair Discrete Systems

Fair discrete systems (FDSs) are a computational model of concurrent programs where fairness assumptions are specified in terms of sets of states. The analysis of fair discrete systems involves a non-trivial interplay between fairness and well-foundedness (ranking functions). This interplay has been an obstacle for automation. The contribution of this paper is a new analysis of temporal properties of FDSs. The analysis uses a domain of binary relations over states labeled by sets of indices of fairness requirements. The use of labeled relations separates the reasoning on well-foundedness and fairness.

[1]  Amir Pnueli,et al.  Algorithmic Verification of Linear Temporal Logic Specifications , 1998, ICALP.

[2]  A. Rybalchenko,et al.  Transition invariants , 2004, LICS 2004.

[3]  Patrick Cousot,et al.  Systematic design of program analysis frameworks , 1979, POPL.

[4]  Amir Pnueli,et al.  Liveness with Invisible Ranking , 2004, VMCAI.

[5]  Patrick Cousot,et al.  Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints , 1977, POPL.

[6]  Christian Holzbaur.  OFAI clp(Q,R) Manual , 1995 .

[7]  Nils Klarlund,et al.  Progress measures and stack assertions for fair termination , 1992, PODC '92.

[8]  Amir Pnueli,et al.  Impartiality, Justice and Fairness: The Ethics of Concurrent Termination , 1981, ICALP.

[9]  Mats Carlsson,et al.  SICStus Prolog User''s Manual , 1993 .

[10]  Andreas Podelski,et al.  A Complete Method for the Synthesis of Linear Ranking Functions , 2004, VMCAI.

[11]  Andreas Podelski,et al.  Transition predicate abstraction and fair termination , 2005, POPL '05.

[12]  Leslie Lamport,et al.  A new solution of Dijkstra's concurrent programming problem , 1974, Commun. ACM.

[13]  Zohar Manna,et al.  Temporal Verification of Reactive Systems , 1995, Springer New York.

[14]  Moshe Y. Vardi.  Verification of Concurrent Programs: The Automata-Theoretic Framework , 1991, Ann. Pure Appl. Log..

[15]  Jan Maluszy¿ski.  Verification, Model Checking, and Abstract Interpretation , 2009, Lecture Notes in Computer Science.

[16]  Amir Pnueli,et al.  Checking that finite state concurrent programs satisfy their linear specification , 1985, POPL.

[17]  Amir Pnueli,et al.  Liveness with Incomprehensible Ranking , 2004, TACAS.

[18]  Patrick Cousot,et al.  Partial Completeness of Abstract Fixpoint Checking , 2000, SARA.

[19]  Henny B. Sipma,et al.  Synthesis of Linear Ranking Functions , 2001, TACAS.

[20]  Ashish Tiwari,et al.  Termination of Linear Programs , 2004, CAV.

[21]  Frank Plumpton Ramsey,et al.  On a Problem of Formal Logic , 1930 .

[22]  Zohar Manna,et al.  Completing the Temporal Picture , 1991, Theor. Comput. Sci..

[23]  Zohar Manna,et al.  Temporal verification of reactive systems - safety , 1995 .