2 research outputs found
Simulations in Rank-Based B\"uchi Automata Complementation (Technical Report)
Complementation of B\"uchi automata is an essential technique used in some
approaches for termination analysis of programs. The long search for an optimal
complementation construction climaxed with the work of Schewe, who proposed a
worst-case optimal rank-based procedure that generates complements of a size
matching the theoretical lower bound of , modulo a polynomial factor
of . Although worst-case optimal, the procedure in many cases produces
automata that are unnecessarily large. In this paper, we propose several ways
of how to use the direct and delayed simulation relations to reduce the size of
the automaton obtained in the rank-based complementation procedure. Our
techniques are based on either (i) ignoring macrostates that cannot be used for
accepting a word in the complement or (ii) saturating macrostates with
simulation-smaller states, in order to decrease their total number. We
experimentally showed that our techniques can indeed considerably decrease the
size of the output of the complementation.Comment: An extended version of a paper to appear in Proc. of APLAS'1
Reducing (to) the Ranks: Efficient Rank-based B\"{u}chi Automata Complementation (Technical Report)
This paper provides several optimizations of the rank-based approach for
complementing B\"{u}chi automata. We start with Schewe's theoretically optimal
construction and develop a set of techniques for pruning its state space that
are key to obtaining small complement automata in practice. In particular, the
reductions (except one) have the property that they preserve (at least some)
so-called super-tight runs, which are runs whose ranking is as tight as
possible. Our evaluation on a large benchmark shows that the optimizations
indeed significantly help the rank-based approach and that, in a large number
of cases, the obtained complement is the smallest from those produced by a
large number of state-of-the-art tools for B\"{u}chi complementation.Comment: Accepted at CONCUR'2