Improved False Causal Loop Detection in Polychronous Specificationof Embedded Software

As opposed to single clocked synchronous programming paradigms, polychronous formalism allows specification of concurrent data flow computation on signals such that various data flows can evolve asynchronous with respect to each other. Explicit constraints and constraints implied by the syntactic structures impart certain intrinsic properties to models specified polychronously. One of the major steps in designing a synthesis engine for polychronous specifications is the characterization of specified models into categories such as inherently sequential or inherently multi-threaded. In this paper, we are concerned with sequentially implementable polychronous specification where computation is divided into a totally ordered sequence of logical instants. Data flow computation within an instant happens based on the implied data flow order. This order or data dependency often varies from one instant to another. Thus determining if there is an instant at which the data flow order forms a causal cycle is an important problem. In the current polychronous compilers, such as SIGNAL compiler and EmCodeSyn, this is solved without due effort, by rejecting any program which has a buffer-free structural cycle. However, a clocked dependency graph can be used to construct logical constraints representing the instants with a possible causal loop. The satisfiability of such constraints would imply that such a loop is realizable and hence the specification has a possible deadlock. The reachability of this instant with a given set of initial conditions would verify if the program should be rejected. In the past, the work on such constraints and their satisfiability has not been implemented even though for pure Boolean signals and clocks this could have been done using a satisfiability solver. With the advent to SAT modulo theory (SMT) solvers, this can now be extended to a more general class of specifications. Moreover, model checking on an abstraction of the specification can provide more information about the reachability of instants at which cyclic data dependency is realized. This paper presents an improved polychronous synthesis tool accepting a much larger class of specifications than could be done before. In our experimental results, we demonstrate the capabilities of our causality analysis methods and show that our synthesis tool performs better than previous strategies, including our own past work.