Model checking of strategic ability under imperfect information is known to be hard. The complexity results range from NP-completeness to undecidability, depending on the precise setup of the problem. No less importantly, fixpoint equivalences do not generally hold for imperfect information strategies, which seriously hampers incremental synthesis of winning strategies.In this paper, we propose translations of ATLir formulae that provide lower and upper bounds for their truth values, and are cheaper to verify than the original specifications. That is, if the expression is verified as true then the corresponding formula of ATLir should also hold in the given model. We begin by showing where the straightforward approach does not work. Then, we propose how it can be modified to obtain guaranteed lower bounds. To this end, we alter the next-step operator in such a way that traversing one's indistinguishability relation is seen as atomic activity. Most interestingly, the lower approximation is provided by a fixpoint expression that uses a nonstandard variant of the next-step ability operator. We show the correctness of the translations, establish their computational complexity, and validate the approach by experiments with a scalable scenario of Bridge play.

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Reversible computation deals with mechanisms for undoing the effects of actions executed by a dynamic system. This paper is concerned with reversibility in the context of Petri nets which are a general formal model of concurrent systems. A key construction we investigate amounts to adding 'reverse' versions of selected net transitions. Such a static modification can severely impact on the behaviour of the system, e.g., the problem of establishing whether the modified net has the same states as the original one is undecidable. We therefore concentrate on nets with finite state spaces and show, in particular, that every transition in such nets can be reversed using a suitable finite set of new transitions.

Reaction systems originated as a formal model for processes inspired by the functioning of the living cell. The underlying idea of this model is that the functioning of the living cell is determined by the interactions of biochemical reactions and these interactions are based on the mechanisms of facilitation and inhibition. Since their inception, reaction systems became a well-investigated novel model of computation. Following this line of research, in this paper we discuss a systematic framework for investigating a whole range of equivalence notions for reaction systems. Some of the equivalences are defined directly on reaction systems while some are defined through transition systems associated with reaction systems. In this way we establish a new bridge between reaction systems and transition systems. In order to define equivalences which capture various ways of interacting with an environment, we also introduce models of the environment which evolve in a finite-state fashion.

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