🤖 AI Summary
This work addresses the model checking problem for Linear Temporal Logic (LTL) formulas under given prior knowledge ( K ), formalized as an LTL formula. We propose a knowledge-guided Büchi automaton simplification method: first constructing a knowledge automaton ( A_K ) from ( K ), then defining and implementing structural reduction of the negated property automaton ( A_{
egvarphi} ) with respect to ( A_K ), yielding an equivalent but significantly smaller Büchi automaton ( B ). Our approach enables direct verification—without constructing the full product automaton ( S otimes A_{
egvarphi} )—for approximately 50% of the MCC’22 benchmark instances. For the remaining cases, ( B ) exhibits substantially fewer states, accelerating emptiness checking. The core contribution lies in formally encoding prior LTL knowledge as an automaton and tightly integrating it into both automaton construction and reduction, thereby enabling semantics-aware acceleration of model checking.
📝 Abstract
We consider the problem of the verification of an LTL specification $varphi$ on a system $S$ given some prior knowledge $K$, an LTL formula that $S$ is known to satisfy. The automata-theoretic approach to LTL model checking is implemented as an emptiness check of the product $Sotimes A_{lnotvarphi}$ where $A_{lnotvarphi}$ is an automaton for the negation of the property. We propose new operations that simplify an automaton $A_{lnotvarphi}$ emph{given} some knowledge automaton $A_K$, to produce an automaton $B$ that can be used instead of $A_{lnotvarphi}$ for more efficient model checking. Our evaluation of these operations on a large benchmark derived from the MCC'22 competition shows that even with simple knowledge, half of the problems can be definitely answered without running an LTL model checker, and the remaining problems can be simplified significantly.