Temporal Logic with Capacity Constraints

Often when modelling systems, physical constraints on the resources available are needed. For example, we might say that at most N processes can access a particular resource at any moment or exactly M participants are needed for an agreement. Such situations are concisely modelled where propositions are constrained such that at most N , or exactly M , can hold at any moment in time. This paper describes both the logical basis and a verification method for propositional linear time temporal logics which allow such constraints as input. The method incorporates ideas developed earlier for a resolution method for the temporal logic TLX and a tableaux-like procedure for PTL. The complexity of this procedure is discussed and case studies are examined. The logic itself represents a combination of standard temporal logic with classical constraints restricting the numbers of propositions that can be satisfied at any moment in time.