Visibly Linear Dynamic Logic [article]

Alexander Weinert, Martin Zimmermann
2017 arXiv   pre-print
We introduce Visibly Linear Dynamic Logic (VLDL), which extends Linear Temporal Logic (LTL) by temporal operators that are guarded by visibly pushdown languages over finite words. In VLDL one can, e.g., express that a function resets a variable to its original value after its execution, even in the presence of an unbounded number of intermediate recursive calls. We prove that VLDL describes exactly the ω-visibly pushdown languages. Thus it is strictly more expressive than LTL and able to
more » ... recursive properties of programs with unbounded call stacks. The main technical contribution of this work is a translation of VLDL into ω-visibly pushdown automata of exponential size via one-way alternating jumping automata. This translation yields exponential-time algorithms for satisfiability, validity, and model checking. We also show that visibly pushdown games with VLDL winning conditions are solvable in triply-exponential time. We prove all these problems to be complete for their respective complexity classes.
arXiv:1512.05177v2 fatcat:f6uldf5zcvcc5craj7nos4s4pm