Abstract-The time separation of events (TSE) problem is that of finding the maximum and minimum separation between the times of occurrence of two events in a concurrent system. It has applications in the performance analysis, optimization and verification of concurrent digital systems. This paper introduces an efficient polynomial-time algorithm to give exact bounds on TSE's for choice-free concurrent systems, whose operational semantics obey the max-causality rule. A choicefree concurrent system is modeled as a strongly-connected marked graph, where delays on operations are modeled as bounded intervals with unspecified distributions. While previous approaches handle acyclic systems only, or else require graph unfolding until a steady-state behavior is reached, the proposed approach directly identifies and evaluates the asymptotic steady-state behavior of a cyclic system via a graph-theoretical approach. As a result, the method has significantly lower computational complexity than previously-proposed solutions. A prototype CAD tool has been developed to demonstrate the feasibility and efficacy of our method. A set of experiments have been performed on the tool as well as two existing tools, with noticeable improvement on runtime and accuracy for several examples.

Hybrid incompatibilities occur when interactions between opposite-ancestry alleles at different loci reduce the fitness of hybrids. Most work on incompatibilities has focused on those that are 'intrinsic', meaning they affect viability and sterility in the laboratory. Theory predicts that ecological selection can also underlie hybrid incompatibilities, but tests of this hypothesis are scarce. In this article, we compiled genetic data for F2 hybrid crosses between divergent populations of threespine stickleback fish (Gasterosteus aculeatus L.) that were born and raised in either the field (semi-natural experimental ponds) or the laboratory (aquaria). We tested for differences in excess heterozygosity between these two environments at ancestry informative loci—a genetic signature of selection against incompatibilities. We found that excess ancestry heterozygosity was elevated by approximately 3% in crosses raised in ponds compared to those raised in aquaria. Previous results from F1 hybrids in the field suggest that pond-specific (single-locus) heterosis is unlikely to explain this finding. Our study suggests that, in stickleback, a coarse signal of environment-dependent hybrid incompatibilities is reliably detectable and that extrinsic incompatibilities have evolved before intrinsic incompatibilities.

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