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Two forms of interferences are individuated in Cardelli and Gordon's Mobile Ambients (MA): plain interferences , which are similar to the interferences one finds in CCS and π-calculus; and grave interferences , which are more dangerous and may be regarded as programming errors. To control interferences, the MA movement primitives are modified; the resulting calculus is called Mobile Safe Ambients (SA).The modification also has computational significance. In the MA interaction rules, an ambient may enter, exit, or open another ambient. The second ambient undergoes the action; it has no control on when the action takes place. In SA this is rectified: any movement takes place only if both participants agree.Existing type systems for MA can be easily adapted to SA. The type systems for controlling mobility, however, appear to be more powerful in SA, in that (i) type systems for MA may give more precise information when transplanted onto SA , and (ii) new type systems may be defined. Two type systems are presented that remove all grave interferences.Other advantages of SA are: a useful algebraic theory; programs sometimes more robust (they require milder conditions for correctness) and/or simpler. All these points are illustrated in several examples.

Reaction systems are a qualitative formalism for modeling systems of biochemical reactions characterized by the non-permanency of the elements: molecules disappear if not produced by any enabled reaction. Moreover, reaction systems execute in an environment that provides new molecules at each step. Brijder, Ehrenfeucht and Rozenberg investigated dynamic causalities in reaction systems by introducing the idea of predictors. A predictor of a molecule s, for a given n, is the set of molecules to be observed in the environment in order to determine whether s is produced or not by the system at step n.\ud \ud In this paper, we continue the investigation on dynamic causalities by defining an abstract interpretation framework containing three different notions of predictor: Formula based predictors, that is a propositional logic formula that precisely characterizes environments that lead to the production of s after n steps; Multi-step based predictors, that consist of n sets of molecules to be observed in the environment, one for each step; and Set based predictors, that are those proposed by Brijder, Ehrenfeucht and Rozenberg, and consist of a unique set of molecules to be observed in all steps.\ud \ud For each kind of predictor we define an effective operator that allows predictors to be computed for any molecule s and number of steps n. The abstract interpretation framework allows us to compare the three notions of predictor in terms of precision, to relate the three defined operators and to compute minimal predictors. We also discuss a generalization of this approach that allows predictors to be defined independently of the value of n, and a tabling approach for the practical use of predictors on reaction systems models. As an application, we use predictors, generalization and tabling to give theoretical grounds to previously obtained results on a model of gene regulation

In this paper we apply the Abstract Interpretation approach [8,9] for approximating the behavior of biological systems, modeled specifically using the Chemical Ground Form calculus [4], a new stochastic calculus rich enough to model the dynamics of biochemical reactions. Our analysis computes an Interval Markov Chain (IMC) that safely approximates the Discrete-Time Markov Chain, describing the probabilistic behavior of the system, and reports both lower and upper bounds for probabilistic temporal properties. Our analysis has several advantages: (i) the method is effective (even for infinite state systems) and allows us to systematically derive an IMC from an abstract labeled transition system; (ii) using intervals for abstracting the multiplicity of reagents allows us to achieve conservative bounds for the concrete probabilities of a set of concrete experiments which differs only for initial concentrations.

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Reaction systems are a qualitative formalism for modeling systems of biochemical reactions characterized by the non-permanency of the elements: molecules disappear if not produced by any enabled reaction. Reaction systems execute in an environment that provides new molecules at each step. Brijder, Ehrenfeucht and Rozemberg introduced the idea of predictors. A predictor of a molecule s, for a given n, is the set of molecules to be observed in the environment to determine whether s is produced or not at step n by the system. We introduced the notion of formula based predictor, that is a propositional logic formula that precisely characterizes environments that lead to the production of s after n steps. In this paper we revise the notion of formula based predictor by defining a specialized version that assumes the environment to provide molecules according to what expressed by a temporal logic formula. As an application, we use specialized formula based predictors to give theoretical grounds to previously obtained results on a model of gene regulation

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