Decidability and complexity for the verification of safety properties of reasonable linear hybrid automata

This paper identifies an industrially relevant class of linear hybrid automata (LHA) called reasonable LHA for which parametric verification of safety properties with exhaustive entry conditions can be done in polynomial time and time-bounded reachability with exhaustive entry conditions can be decided in nondeterministic polynomial time for non-parametric verification and in exponential time for parametric verification. Deciding whether an LHA is reasonable is shown to be decidable in polynomial time.

[1]  Eduardo D. Sontag,et al.  Real Addition and the Polynomial Hierarchy , 1985, Inf. Process. Lett..

[2]  G. J. Tee,et al.  Khachian's efficient algorithm for linear inequalities and linear programming , 1980, SGNM.

[3]  André Platzer,et al.  European Train Control System: A Case Study in Formal Verification , 2009, ICFEM.

[4]  Spiros Skiadopoulos,et al.  Querying temporal and spatial constraint networks in PTIME , 2000, Artif. Intell..

[5]  Joseph S. Miller.  Decidability and Complexity Results for Timed Automata and Semi-linear Hybrid Automata , 2000, HSCC.

[6]  Farn Wang.  Symbolic Parametric Safety Analysis of Linear Hybrid Systems with BDD-Like Data-Structures , 2004, CAV.

[7]  Stefan Ratschan,et al.  Guaranteed Termination in the Verification of LTL Properties of Non-linear Robust Discrete Time Hybrid Systems , 2005, ATVA.

[8]  Viorica Sofronie-Stokkermans,et al.  Hierarchic Reasoning in Local Theory Extensions , 2005, CADE.

[9]  André Platzer,et al.  Logical Verification and Systematic Parametric Analysis in Train Control , 2008, HSCC.

[10]  George J. Pappas,et al.  Robustness of Temporal Logic Specifications , 2006, FATES/RV.

[11]  Sanjit A. Seshia,et al.  Symbolic Reachability Analysis of Lazy Linear Hybrid Automata , 2007, FORMATS.

[12]  Thomas Brihaye,et al.  On the expressiveness and decidability of o-minimal hybrid systems , 2005, J. Complex..

[13]  Jan Lunze,et al.  Handbook of hybrid systems control : theory, tools, applications , 2009 .

[14]  Sumit Kumar Jha,et al.  A Counterexample-Guided Approach to Parameter Synthesis for Linear Hybrid Automata , 2008, HSCC.

[15]  Bernhard Nebel,et al.  Reasoning about temporal relations: a maximal tractable subclass of Allen's interval algebra , 1994, JACM.

[16]  G. Frehse.  Handbook of Hybrid Systems Control: Verification tools for linear hybrid automata , 2009 .

[17]  Pravin Varaiya,et al.  What's decidable about hybrid automata? , 1995, STOC '95.

[18]  Narendra Karmarkar,et al.  A new polynomial-time algorithm for linear programming , 1984, Comb..

[19]  Martin Fränzle,et al.  A Symbolic Decision Procedure for Robust Safety of Timed Systems , 2007, 14th International Symposium on Temporal Representation and Reasoning (TIME'07).

[20]  T. Henzinger,et al.  Algorithmic Analysis of Nonlinear Hybrid Systems , 1998, CAV.

[21]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[22]  Carsten Ihlemann,et al.  System Description: H-PILoT , 2009, CADE.

[23]  Henning Dierks,et al.  Exact and fully symbolic verification of linear hybrid automata with large discrete state spaces , 2012, Sci. Comput. Program..

[24]  Nikolaj Bjørner,et al.  Z3: An Efficient SMT Solver , 2008, TACAS.

[25]  S. Shankar Sastry,et al.  O-Minimal Hybrid Systems , 2000, Math. Control. Signals Syst..

[26]  Manolis Koubarakis,et al.  Tractable disjunctions of linear constraints: basic results and applications to temporal reasoning , 2001, Theor. Comput. Sci..

[27]  Gerardo Lafferriere,et al.  A New Class of Decidable Hybrid Systems , 1999, HSCC.

[28]  Sumit Gulwani,et al.  Constraint-Based Approach for Analysis of Hybrid Systems , 2008, CAV.

[29]  Viorica Sofronie-Stokkermans.  Efficient Hierarchical Reasoning about Functions over Numerical Domains , 2008, KI.

[30]  Thomas A. Henzinger,et al.  Automatic symbolic verification of embedded systems , 1993, 1993 Proceedings Real-Time Systems Symposium.

[31]  Viorica Sofronie-Stokkermans.  Hierarchical Reasoning for the Verification of Parametric Systems , 2010, IJCAR.

[32]  P. S. Thiagarajan,et al.  The Discrete Time Behavior of Lazy Linear Hybrid Automata , 2005, HSCC.

[33]  Thomas Sturm,et al.  REDLOG: computer algebra meets computer logic , 1997, SIGS.