SigmaK-constraints for Hybrid Systems

In this paper we introduce and study computational aspects of $\it \Sigma_K$-constraints which are powerful enough to represent computable continuous data, but also simple enough to be an approach to approximate constraint solving for a large class of quantified continuous constraints. We illustrate how $\it \Sigma_K$-constraints can be used for reasoning about hybrid systems.

[1]  Oleg V. Kudinov,et al.  Characteristic Properties of Majorant-Computability over the Reals , 1998, CSL.

[2]  Benedikt Löwe,et al.  New Computational Paradigms , 2005 .

[3]  S. Basu,et al.  Algorithms in real algebraic geometry , 2003 .

[4]  Robert L. Grossman,et al.  Timed Automata , 1999, CAV.

[5]  I︠U︡riĭ Leonidovich Ershov.  Definability and Computability , 1996 .

[6]  Thomas A. Henzinger,et al.  Hybrid Systems: Computation and Control , 1998, Lecture Notes in Computer Science.

[7]  Frank Wolter,et al.  Monodic fragments of first-order temporal logics: 2000-2001 A.D , 2001, LPAR.

[8]  Andreas Blass,et al.  Background, Reserve, and Gandy Machines , 2000, CSL.

[9]  Klaus Weihrauch,et al.  Computability on Subsets of Euclidean Space I: Closed and Compact Subsets , 1999, Theor. Comput. Sci..

[10]  Oleg V. Kudinov,et al.  Semantic Characterisations of Second-Order Computability over the Real Numbers , 2001, CSL.

[11]  A Pettorossi.  Automata theory and formal languages , 2008 .

[12]  Margarita V. Korovina,et al.  Gandy's Theorem for Abstract Structures without the Equality Test , 2003, LPAR.

[13]  Marc Christie,et al.  Interval constraint solving for camera control and motion planning , 2000, TOCL.

[14]  Thomas A. Henzinger,et al.  Reachability Verification for Hybrid Automata , 1998, HSCC.

[15]  Johann A. Makowsky,et al.  Query Languages for Hierarchic Databases , 1992, Inf. Comput..

[16]  Oleg V. Kudinov,et al.  Towards Computability of Higher Type Continuous Data , 2005, CiE.

[17]  Oleg V. Kudinov,et al.  Towards Computability over Effectively Enumerable Topological Spaces , 2008, CCA.

[18]  Manfred Broy,et al.  Perspectives of System Informatics , 2001, Lecture Notes in Computer Science.

[19]  Klaus Weihrauch,et al.  Computable Analysis: An Introduction , 2014, Texts in Theoretical Computer Science. An EATCS Series.

[20]  Peter Hertling,et al.  Computability & Complexity in Analysis , 2001 .

[21]  Ashish Tiwari,et al.  Abstractions for hybrid systems , 2008, Formal Methods Syst. Des..

[22]  B. F. Caviness,et al.  Quantifier Elimination and Cylindrical Algebraic Decomposition , 2004, Texts and Monographs in Symbolic Computation.

[23]  Jon Barwise,et al.  Admissible sets and structures , 1975 .

[24]  George E. Collins,et al.  Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition , 1975, Automata Theory and Formal Languages.

[25]  Stefan Ratschan,et al.  Constraints for Continuous Reachability in the Verification of Hybrid Systems , 2006, AISC.

[26]  Anil Nerode,et al.  Models for Hybrid Systems: Automata, Topologies, Controllability, Observability , 1992, Hybrid Systems.

[27]  Alex K. Simpson,et al.  Computational Adequacy in an Elementary Topos , 1998, CSL.

[28]  Margarita V. Korovina,et al.  Computational Aspects of sigma-Definability over the Real Numbers without the Equality Test , 2003, CSL.

[29]  Bart De Schutter.  Models for Hybrid Systems , 2005 .

[30]  Oleg V. Kudinov,et al.  Generalised Computability and Applications to Hybrid Systems , 2001, Ershov Memorial Conference.

[31]  Andrei S. Morozov,et al.  Remarks on Sigma-definability without the equality test over the Reals , 2008, CCA.

[32]  Marian Boykan Pour-El,et al.  Computability in analysis and physics , 1989, Perspectives in Mathematical Logic.

[33]  Hirokazu Anai,et al.  Reach Set Computations Using Real Quantifier Elimination , 2001, HSCC.

[34]  Oleg V. Kudinov,et al.  Formalisation of Computability of Operators and Real-Valued Functionals via Domain Theory , 2000, CCA.