Safraless Synthesis for Epistemic Temporal Specifications

March 16, 2015

Rodica Bozianu (LACL - UPEC)

We address the synthesis problem for specifications given in linear temporal single agent epistemic logic, KLTL, over single-agent systems having imperfect information of the environment state. R. van der Meyden and M. Vardi have shown that this problem is 2Exptime complete. However, their procedure relies on complex automata constructions that are notoriously resistant to efficient implementations as they use Safra-like determinization.

We propose a ”Safraless” synthesis procedure for a large fragment of KLTL. The construction transforms first the synthesis problem into theproblem of checking emptiness for universal co-Büchi tree automata using an information-set construction. Then we build a safety game that can be solved using an antichain-based symbolic technique exploiting the structure of the underlying automata. The technique is implemented and applied to a couple of case studies.

Further, we try to extend the procedure for the entire KLTL by defining automata accepting sets of words satisfying KLTL formula. We use the J. M. Couvreur’s construction of Büchi automata for LTL formulas and extend it to accept sets of words satisfying KLTL formulas.