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MOTIVATION Thousands of proteins are known to bind to DNA; for most of them the mechanism of action and the residues that bind to DNA, i.e. the binding sites, are yet unknown. Experimental identification of binding sites requires expensive and laborious methods such as mutagenesis and binding essays. Hence, such studies are not applicable on a large scale.… (More)
Agent-based models (ABMs) / multi-agent systems (MASs) are today one of the most widely used modeling– simulation–analysis approaches for understanding the dy-namical behavior of complex systems. These models are often characterized by several parameters with nonlinear interactions which together determine the global system dynamics, usually measured by… (More)
In this paper, we suggest a possible confluence of the theory of hybrid automata and the techniques of algorithmic algebra to create a computational basis for systems biology. We describe a method to compute bounded reachability by combining Taylor polynomials and cylindric algebraic decomposition algorithms. We discuss the power and limitations of the… (More)
Motivated by applications to systems biology, and the emergence of semi-algebraic hybrid systems as a natural framework for model-ing biochemical networks, we continue exploring the decidability problem for model-checking with TCTL (Timed Computation Tree Logic) over this broad class of semi-algebraic hybrid systems. Previously, we had introduced these… (More)
A series of papers, all under the title of Algorithmic Algebraic Model Checking (AAMC), has sought to combine techniques from algorithmic algebra , model checking and dynamical systems to examine how a biochemical hybrid dynamical system can be made amenable to temporal analysis, even when the initial conditions and unknown parameters may only be treated as… (More)
We present computationally efficient techniques for approximate model-checking using bisimulation-partitioning, polyhedra, grids and time discretization for semi-algebraic hybrid systems, and demonstrate how they relate to and extend other existing techniques.
Even though many attempts have been made to define the boundary between decid-able and undecidable hybrid systems, the affair is far from being solved. More and more low dimensional systems are being shown to be undecidable with respect to reachability, and many open problems in between are being discovered. In this paper , we present various two… (More)