To be fair, use bundles

Attempts to manage the reasoning about systems with fairness properties are long running. The popular but restricted Computational Tree Logic (CTL) is amenable to automated reasoning but has difficulty expressing some fairness properties. More expressive languages such as CTL* and CTL+ are computationally complex. The main contribution of this paper is to show the usefulness and practicality of employing the bundled variants of these languages to handle fairness. In particular we present a tableau for a bundled variant of CTL that still has the similar computational complexity to the CTL tableau and a simpler implementation. We further show that the decision problem remains in EXPTIME even if a bounded number of CTL* fairness constraints are allowed in the input formulas. By abandoning limit closure the bundled logics can simultaneously be easier to automate and express many typical fairness constraints.

[1]  E. Allen Emerson,et al.  The Complexity of Tree Automata and Logics of Programs , 1999, SIAM J. Comput..

[2]  Thomas Wilke,et al.  CTL+ is Exponentially more Succinct than CTL , 1999, FSTTCS.

[3]  John Christopher McCabe-Dansted.  A Rooted Tableau for BCTL* , 2011, Electron. Notes Theor. Comput. Sci..

[4]  A. Prasad Sistla,et al.  Deciding Branching Time Logic: A Triple Exponential Decision Procedure for CTL* , 1983, Logic of Programs.

[5]  Pierre Wolper,et al.  Reasoning about fair concurrent programs , 1986, STOC '86.

[6]  Joseph Y. Halpern,et al.  Decision procedures and expressiveness in the temporal logic of branching time , 1982, STOC '82.

[7]  Edmund M. Clarke,et al.  Characterizing Finite Kripke Structures in Propositional Temporal Logic , 1988, Theor. Comput. Sci..

[8]  Rajeev Goré,et al.  An Experimental Comparison of Theorem Provers for CTL , 2011, 2011 Eighteenth International Symposium on Temporal Representation and Reasoning.

[9]  Will Marrero,et al.  Using BDDs to Decide CTL , 2005, TACAS.

[10]  Alexander Bolotov,et al.  A clausal resolution method for branching-time logic ECTL+ , 2004, Proceedings. 11th International Symposium on Temporal Representation and Reasoning, 2004. TIME 2004..

[11]  Saharon Shelah,et al.  On the temporal analysis of fairness , 1980, POPL '80.

[12]  Jan Johannsen,et al.  CTL+ Is Complete for Double Exponential Time , 2003, ICALP.

[13]  Saharon Shelah,et al.  Reasoning with Time and Chance , 1982, Inf. Control..

[14]  Oliver Friedmann,et al.  A Decision Procedure for CTL* Based on Tableaux and Automata , 2010, IJCAR.

[15]  John Christopher McCabe-Dansted,et al.  A Tableau for the Combination of CTL and BCTL , 2012, 2012 19th International Symposium on Temporal Representation and Reasoning.

[16]  Mark Reynolds,et al.  A Tableau for Bundled CTL , 2006, J. Log. Comput..

[17]  Joseph Y. Halpern,et al.  “Sometimes” and “not never” revisited: on branching versus linear time temporal logic , 1986, JACM.

[18]  Chin-Laung Lei,et al.  Modalities for Model Checking: Branching Time Logic Strikes Back , 1987, Sci. Comput. Program..

[19]  Jamal Bentahar,et al.  Verifying concurrent probabilistic systems using probabilistic-epistemic logic specifications , 2016, Applied Intelligence.

[20]  Mordechai Ben-Ari,et al.  The temporal logic of branching time , 1981, POPL '81.

[21]  Luca Viganò,et al.  Labelled natural deduction for a bundled branching temporal logic , 2011, J. Log. Comput..

[22]  Edmund M. Clarke,et al.  Sequential circuit verification using symbolic model checking , 1991, DAC '90.

[23]  A. Prasad Sistla,et al.  Deciding branching time logic , 1984, STOC '84.

[24]  Clare Dixon,et al.  A resolution calculus for the branching-time temporal logic CTL , 2014, ACM Trans. Comput. Log..

[25]  Larry J. Stockmeyer,et al.  Improved upper and lower bounds for modal logics of programs , 1985, STOC '85.

[26]  Mark Reynolds,et al.  A tableau-based decision procedure for CTL* , 2011, Formal Aspects of Computing.