Abstract interpretation and application to logic programs
Journal of Logic Programming
Types as abstract interpretations
Proceedings of the 24th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Modeling Dynamic Phenomena in Molecular and Cellular Biology
Modeling Dynamic Phenomena in Molecular and Cellular Biology
Constructive design of a hierarchy of semantics of a transition system by abstract interpretation
Theoretical Computer Science
Petri Net Representations in Metabolic Pathways
Proceedings of the 1st International Conference on Intelligent Systems for Molecular Biology
Symbolic Model Checking of Biochemical Networks
CMSB '03 Proceedings of the First International Workshop on Computational Methods in Systems Biology
Typing constraint logic programs
Theory and Practice of Logic Programming
Modeling and querying biomolecular interaction networks
Theoretical Computer Science - Special issue: Computational systems biology
Machine learning biochemical networks from temporal logic properties
Transactions on Computational Systems Biology VI
CMBSlib: a library for comparing formalisms and models of biological systems
CMSB'04 Proceedings of the 20 international conference on Computational Methods in Systems Biology
CMSB'04 Proceedings of the 20 international conference on Computational Methods in Systems Biology
From syntax to semantics in systems biology towards automated reasoning tools
Transactions on Computational Systems Biology IV
From Reaction Models to Influence Graphs and Back: A Theorem
FMSB '08 Proceedings of the 1st international workshop on Formal Methods in Systems Biology
Formal cell biology in biocham
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
Steady-state solution of biochemical systems, beyond S-systems via T-invariants
Proceedings of the 8th International Conference on Computational Methods in Systems Biology
Fundamenta Informaticae - From Mathematical Beauty to the Truth of Nature: to Jerzy Tiuryn on his 60th Birthday
Dynamically consistent reduction of logical regulatory graphs
Theoretical Computer Science
WMC'09 Proceedings of the 10th international conference on Membrane Computing
Typed stochastic semantics for the calculus of looping sequences
Theoretical Computer Science
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Abstract interpretation is a theory of abstraction that has been introduced for the analysis of programs. In particular, it has proved useful for organizing the multiple semantics of a given programming language in a hierarchy corresponding to different detail levels, and for defining type systems for programming languages and program analyzers in software engineering. In this paper, we investigate the application of these concepts to systems biology formalisms. More specifically, we consider the Systems Biology Markup Language SBML, and the Biochemical Abstract Machine BIOCHAM with its differential, stochastic, discrete and boolean semantics. We first show how all of these different semantics, except the differential one, can be formally related by simple Galois connections. Then we define three type systems: one for checking or inferring the functions of proteins in a reaction model, one for checking or inferring the activation and inhibition effects of proteins in a reaction model, and another one for checking or inferring the topology of compartments or locations. We show that the framework of abstract interpretation elegantly applies to the formalization of these further abstractions, and to the implementation of linear or quadratic time type checking as well as type inference algorithms. Furthermore, we show a theorem of independence of the graph of activation and inhibition effects from the kinetic expressions in the reaction model, under general conditions. Through some examples, we show that the analysis of biochemical models by type inference provides accurate and useful information. Interestingly, such a mathematical formalization of the abstractions commonly used in systems biology already provides some guidelines for the extensions of biochemical reaction rule languages.