Operator precedence temporal logic and model checking

Abstract

In the last decades much research effort has been devoted to extending the success of model checking from the traditional field of finite state machines and various versions of temporal logics to suitable subclasses of context-free languages and appropriate extensions of temporal logics. To the best of our knowledge such attempts only covered structured languages, i.e. languages whose structure is immediately "visible" in their sentences, such as tree-languages or visibly pushdown ones. In this paper we present a new temporal logic suitable to express and automatically verify properties of operator precedence languages. This "historical" language family has been recently proved to enjoy fundamental algebraic and logic properties that make it suitable for model checking applications yet breaking the barrier of visible-structure languages (in fact the original motivation of its inventor Floyd was just to support efficient parsing, i.e. building the "hidden syntax tree" of language sentences). We prove that our logic is at least as expressive as analogous logics defined for visible pushdown languages yet covering a much more powerful family; we design a procedure that, given a formula in our logic builds an automaton recognizing the sentences satisfying the formula, whose size is at most exponential in the length of the formula. Our results cover both finite and infinite string languages.

Model-Checking Structured Context-Free Languages

“…It is in some sense a theoretical assurance of the sufficient expressive power of the logic. Moreover, NWTL ⊂ OPTL was proved in [22], and OPTL ⊆ POTL comes from Theorem 1 and the semantics of OPTL being expressible in FOL. In [23], we also prove that there exist POTL formulas not expressible in OPTL.…”

“…To reason about such behaviors, temporal logics based on Operator Precedence Languages (OPL) have been proposed [22]. OPL were initially introduced with the purpose of efficient parsing [31], a field in which they continue to offer useful applications [11].…”

“…OPTL [22] is the first linear-time temporal logic for which a model checking procedure has been given on both finite and ω-words of OPL. It enables reasoning on procedural programs with exceptions, expressing properties about whether a function can be terminated by an exception, or throw one, and also pre/postconditions.…”

“…NWTL can be translated into OPTL in linear time, thus the latter is capable of expressing all properties that can be formalized in CaRet and NWTL, and many more. [22] does not explore OPTL's expressiveness further, and does not investigate the practical applicability of their model checking construction.…”

Model Checking Temporal Properties of Recursive Probabilistic Programs

“…by generalizing the automata-less LTL model checking algorithm from [30]. Other topics are to investigate to what extent algorithms for probabilistic CTL can be generalized to the branching-time variant of CaReT [18], or to consider more expressive logics than CaReT such as visibly LTL [7] and the operator precedence temporal logic [11].…”