Automatic verification of finite-state concurrent systems using temporal logic specifications
ACM Transactions on Programming Languages and Systems (TOPLAS)
Ordinary Differential Equations
Ordinary Differential Equations
Hybridization methods for the analysis of nonlinear systems
Acta Informatica - Hybrid Systems
Automatica (Journal of IFAC)
Approximating Continuous Systems by Timed Automata
FMSB '08 Proceedings of the 1st international workshop on Formal Methods in Systems Biology
Communications of the ACM - Security in the Browser
Temporal Logic Patterns for Querying Qualitative Models of Genetic Regulatory Networks
Proceedings of the 2008 conference on ECAI 2008: 18th European Conference on Artificial Intelligence
Computing Reachable States for Nonlinear Biological Models
CMSB '09 Proceedings of the 7th International Conference on Computational Methods in Systems Biology
Computational Analysis of Large-Scale Multi-affine ODE Models
HIBI '09 Proceedings of the 2009 International Workshop on High Performance Computational Systems Biology
MARCO: a reachability algorithm for multi-affine systems with applications to biological systems
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
Automatic rectangular refinement of affine hybrid systems
FORMATS'05 Proceedings of the Third international conference on Formal Modeling and Analysis of Timed Systems
A control problem for affine dynamical systems on a full-dimensional polytope
Automatica (Journal of IFAC)
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This is an extended version of the workshop paper [1], in which a new computational technique called quantitative discrete approximation has been introduced. The technique provides finite discrete approximation of continuous dynamical systems which is suitable especially for a significant class of biochemical dynamical systems. With decreasing granularity the approximation of behaviour between a discrete state and its successor converges to the behaviour of the original continuous system in the respective part of the phase space. This paper provides a detailed description of the method and algorithms solving the reachability problem in biochemical dynamical systems. The method is supplemented with heuristics for reducing the cardinality of the reachable state space. The algorithms are evaluated on six models (with numbers of variables ranging from 2 to 12).