Delays in biological systems may appear at any level of detail of the modeled system, in particular delays may be used to model events for which the underline dynamics can not be completely observed. There exist constant and variable (e.g. time–dependent, state–dependent) forms of delays and different modeling techniques for
In this thesis we address the problem of formal modeling biological systems with delays in all their variants and interpretations.
In the ﬁrst part of the thesis we introduce the framework for deterministic modeling of biological systems (e.g. Delay Differential Equations) and we deﬁne Delayed Chemical Master
Equations. In complete accordance with the standard approach for formal modeling biological systems without delays, we also extend the framework for stochastic modeling by deﬁning some variants of Delayed Stochastic Simulation Algorithms (DSSAs). We also investigate these DSSAs in order to define, if possible, equivalence properties.
In the second part of the thesis we address the problem of both qualitative and quantitative formal modeling of biological systems with delays by using existing formal languages theory and by extending well–known formal languages for modeling biological systems without delays. In particular, we will define formal languages based on the previously specified interpretation of delays.