A Decision Procedure for a Fragment of Linear Time Mu-Calculus

In this paper, we study an expressive fragment, namely Gµ, of linear time µ-calculus as a high-level goal specification language. We define Goal Progression Form (GPF) for Gµ formulas and show that every closed formula can be transformed into this form. Based on GPF, we present the notion of Goal Progression Form Graph (GPG) which can be used to describe models of a formula. Further, we propose a simple and intuitive GPG-based decision procedure for checking satisfiability of Gµ formulas which has the same time complexity as the decision problem of Linear Temporal Logic (LTL). However, Gµ is able to express a wider variety of temporal goals compared with LTL.

[1]  Jorge A. Baier,et al.  Polynomial-Time Reformulations of LTL Temporally Extended Goals into Final-State Goals , 2015, IJCAI.

[2]  Richard E. Ladner,et al.  Propositional Dynamic Logic of Regular Programs , 1979, J. Comput. Syst. Sci..

[3]  E. Allen Emerson,et al.  The Propositional Mu-Calculus is Elementary , 1984, ICALP.

[4]  J. van Leeuwen,et al.  Theoretical Computer Science , 2003, Lecture Notes in Computer Science.

[5]  Emilio Frazzoli,et al.  Sampling-based motion planning with deterministic μ-calculus specifications , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[6]  Martin Hofmann,et al.  A Proof System for the Linear Time µ-Calculus , 2006, FSTTCS.

[7]  Edmund M. Clarke,et al.  Characterizing Correctness Properties of Parallel Programs Using Fixpoints , 1980, ICALP.

[8]  Diego Calvanese,et al.  Reasoning about Actions and Planning in LTL Action Theories , 2002, KR.

[9]  Roope Kaivola.  A Simple Decision Method for the Linear Time Mu-calculus , 1995, STRICT.

[10]  Howard Barringer,et al.  Temporal Logic with Fixed Points , 1987, Temporal Logic in Specification.

[11]  S. Tsur.  Annals of Mathematics and Artificial Intelligence , 2004, Annals of Mathematics and Artificial Intelligence.

[12]  Amir Pnueli,et al.  The temporal logic of programs , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[13]  Jorge A. Baier,et al.  Planning with First-Order Temporally Extended Goals using Heuristic Search , 2006, AAAI.

[14]  Dexter Kozen,et al.  Results on the Propositional µ-Calculus , 1982, ICALP.

[15]  Oliver Friedmann,et al.  On guarded transformation in the modal μ-calculus , 2015, Log. J. IGPL.

[16]  Giuseppe De Giacomo,et al.  Automata-Theoretic Approach to Planning for Temporally Extended Goals , 1999, ECP.

[17]  Javier Esparza,et al.  An Effective Tableau System for the Linear Time µ-Calculus , 1996, ICALP.

[18]  Moshe Y. Vardi.  A temporal fixpoint calculus , 1988, POPL '88.

[19]  A. Paul,et al.  Pacific Journal of Mathematics , 1999 .

[20]  Stephen Cresswell,et al.  Compilation of LTL Goal Formulas into PDDL , 2004, ECAI.

[21]  Giuseppe De Giacomo,et al.  Computing Infinite Plans for LTL Goals Using a Classical Planner , 2011, IJCAI.

[22]  David Walker,et al.  CCS, Liveness, and Local Model Checking in the Linear Time Mu-Calculus , 1989, Automatic Verification Methods for Finite State Systems.

[23]  M. Panella.  Associate Editor of the Journal of Computer and System Sciences , 2014 .

[24]  Giuseppe De Giacomo,et al.  Linear Temporal Logic and Linear Dynamic Logic on Finite Traces , 2013, IJCAI.

[25]  Stefan Edelkamp,et al.  On the Compilation of Plan Constraints and Preferences , 2006, ICAPS.

[26]  Fahiem Bacchus,et al.  Planning for temporally extended goals , 1996, Annals of Mathematics and Artificial Intelligence.

[27]  Li Zhang,et al.  A decision procedure for propositional projection temporal logic with infinite models , 2008, Acta Informatica.

[28]  A. Tarski.  A LATTICE-THEORETICAL FIXPOINT THEOREM AND ITS APPLICATIONS , 1955 .

[29]  Cong Tian,et al.  A canonical form based decision procedure and model checking approach for propositional projection temporal logic , 2016, Theor. Comput. Sci..

[30]  Jussi Rintanen,et al.  Incorporation of Temporal Logic Control into Plan Operators , 2000, ECAI.

[31]  DuanZhenhua,et al.  A canonical form based decision procedure and model checking approach for propositional projection temporal logic , 2016 .

[32]  Amir Pnueli,et al.  A really abstract concurrent model and its temporal logic , 1986, POPL '86.

[33]  Sylvie Thiébaux,et al.  Search Control in Planning for Temporally Extended Goals , 2005, ICAPS.

[34]  Peter Kulchyski.  and , 2015 .

[35]  Giuseppe De Giacomo,et al.  Synthesis for LTL and LDL on Finite Traces , 2015, IJCAI.

[36]  Cong Tian,et al.  A practical decision procedure for Propositional Projection Temporal Logic with infinite models , 2014, Theor. Comput. Sci..

[37]  Dexter Kozen,et al.  RESULTS ON THE PROPOSITIONAL’p-CALCULUS , 2001 .

[38]  Dan Suciu,et al.  Journal of the ACM , 2006 .