Handbook of theoretical computer science (vol. B)
Concurrent constraint programming
Concurrent constraint programming
Theoretical Computer Science
State Equivalences for Rectangular Hybrid Automata
CONCUR '96 Proceedings of the 7th International Conference on Concurrency Theory
Decidability of Hybrid Systems with Rectangular Differential Inclusion
CAV '94 Proceedings of the 6th International Conference on Computer Aided Verification
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Computing simulations on finite and infinite graphs
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
The theory of rectangular hybrid automata
The theory of rectangular hybrid automata
Fluid Flow Approximation of PEPA models
QEST '05 Proceedings of the Second International Conference on the Quantitative Evaluation of Systems
Model checking liveness properties of genetic regulatory networks
TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
Algorithmic algebraic model checking i: challenges from systems biology
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
A compositional approach to the stochastic dynamics of gene networks
Transactions on Computational Systems Biology IV
Discrete Semantics for Hybrid Automata
Discrete Event Dynamic Systems
Hybrid dynamics of stochastic programs
Theoretical Computer Science
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Hybrid Systems are dynamical systems presenting both discrete and continuous evolution. Hybrid Automata are a formal model for hybrid systems, originally proposed to study embedded systems, where a discrete control acts on a continuously changing environment. The presence of both discrete and continuous dynamics makes this formalism appealing also for modeling biological systems. However, the situation in this case is subtler, as there is no natural separation into discrete and continuous components. No surprise, then, that hybrid automata have been used in systems biology in rather different ways. Some approaches, like the description of biological switches, concentrate on the use of model-checking routines. Other applications, like the switching between continuous and discrete/stochastic simulation, focus on the exploitation of the interplay between discreteness and continuity in order to reduce the computational burden of numerical simulation, yet maintaining an acceptable precision. We will survey the use of hybrid automata in systems biology, through a series of cases studies that we deem interesting and paradigmatic.