Achieving while maintaining:A logic of knowing how with intermediate constraints

In this paper, we propose a ternary knowing how operator to express that the agent knows how to achieve $\phi$ given $\psi$ while maintaining $\chi$ in-between. It generalizes the logic of goal-directed knowing how proposed by Yanjing Wang 2015 'A logic of knowing how'. We give a sound and complete axiomatization of this logic.Comment: appear in Proceedings of ICLA 201

Efficient Büchi Universality Checking

The complementation of Büchi automata, required for checking automata universality, remains one of the outstanding automata-theoretic challenges in formal verification. Early constructions using a Ramsey-based argument have been supplanted by rank-based constructions with exponentially better bounds. The best rank-based algorithm for Büchi universality, by Doyen and Raskin, employs a subsumption technique to minimize the size of the working set. Separately, in the context of program termination, Lee et al. have specialized the Ramsey-based approach to size-change termination (SCT) problems. In this context, Ramsey-based algorithms have proven to be surprisingly competitive. The strongest tool, from Ben-Amram and Lee, also uses a subsumption technique, although only for the special case of SCT problems. We extend the subsumption technique of Ben-Amram and Lee to the general case of Büchi universality problems, and experimentally demonstrate the necessity of subsumption for the scalability of the Ramsey-based approach. We then empirically compare the Ramsey-based tool to the rank-based tool of Doyen and Raskin over a terrain of random Büchi universality problems. We discover that the two algorithms exhibit distinct behavior over this problem terrain. As expected, on many of the most difficult areas the rank-based approach provides the superior tool. Surprisingly, there also exist several areas, including the area most difficult for rank-based tools, on which the Ramsey-based solver scales better than the rank-based solver. This result demonstrates the pitfalls of using worst-case complexity to evaluate algorithms. We suggest that a portfolio approach may be the best approach to checking the universality of Büchi automata