Complexity of deciding Tarski algebra
Journal of Symbolic Computation
Theoretical Computer Science
The algorithmic analysis of hybrid systems
Theoretical Computer Science - Special issue on hybrid systems
What's decidable about hybrid automata?
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
On the combinatorial and algebraic complexity of quantifier elimination
Journal of the ACM (JACM)
A Calculus of Communicating Systems
A Calculus of Communicating Systems
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Decidability of Hybrid Systems with Rectangular Differential Inclusion
CAV '94 Proceedings of the 6th International Conference on Computer Aided Verification
Proceedings of the Real-Time: Theory in Practice, REX Workshop
The d/dt Tool for Verification of Hybrid Systems
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
An Improved Algorithm for Quantifier Elimination Over Real Closed Fields
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
The theory of rectangular hybrid automata
The theory of rectangular hybrid automata
Proceedings of the 38th conference on Winter simulation
Approximate bisimulation relations for constrained linear systems
Automatica (Journal of IFAC)
Petri net modelling of biological regulatory networks
Journal of Discrete Algorithms
Approximate Simulation Relations for Hybrid Systems
Discrete Event Dynamic Systems
Brief paper: Hierarchical control system design using approximate simulation
Automatica (Journal of IFAC)
Introduction to Mathematical Logic
Introduction to Mathematical Logic
Automated symbolic reachability analysis: with application to delta-notch signaling automata
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
Hybrid systems and biology: continuous and discrete modeling for systems biology
SFM'08 Proceedings of the Formal methods for the design of computer, communication, and software systems 8th international conference on Formal methods for computational systems biology
Behavioural approximations for restricted linear differential hybrid automata
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
ATVA'05 Proceedings of the Third international conference on Automated Technology for Verification and Analysis
Algorithmic algebraic model checking i: challenges from systems biology
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
Beta binders for biological interactions
CMSB'04 Proceedings of the 20 international conference on Computational Methods in Systems Biology
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Many natural systems exhibit a hybrid behavior characterized by a set of continuous laws which are switched by discrete events. Such behaviors can be described in a very natural way by a class of automata called hybrid automata. Their evolution are represented by both dynamical systems on dense domains and discrete transitions. Once a real system is modeled in a such framework, one may want to analyze it by applying automatic techniques, such as Model Checking or Abstract Interpretation. Unfortunately, the discrete/continuous evolutions not only provide hybrid automata of great flexibility, but they are also at the root of many undecidability phenomena. This paper addresses issues regarding the decidability of the reachability problem for hybrid automata (i.e., "can the system reach a state a from a state b?") by proposing an "inaccurate" semantics. In particular, after observing that dense sets are often abstractions of real world domains, we suggest, especially in the context of biological simulation, to avoid the ability of distinguishing between values whose distance is less than a fixed 驴. On the ground of the above considerations, we propose a new semantics for first-order formulæ which guarantees the decidability of reachability. We conclude providing a paradigmatic biological example showing that the new semantics mimics the real world behavior better than the precise one.