Counterexample-Preserving Reduction for Symbolic Model Checking

The cost of LTL model checking is highly sensitive to the length of the formula under verification. We observe that, under some specific conditions, the input LTL formula can be reduced to an easier-to-handle one before model checking. In our reduction, these two formulae need not to be logically equivalent, but they share the same counterexample set w.r.t the model. In the case that the model is symbolically represented, the condition enabling such reduction can be detected with a lightweight effort (e.g., with SAT-solving). In this paper, we tentatively name such technique "Counterexample-Preserving Reduction" (CePRe for short), and finally the proposed technquie is experimentally evaluated by adapting NuSMV

Almost Linear B\"uchi Automata

We introduce a new fragment of Linear temporal logic (LTL) called LIO and a new class of Buechi automata (BA) called Almost linear Buechi automata (ALBA). We provide effective translations between LIO and ALBA showing that the two formalisms are expressively equivalent. While standard translations of LTL into BA use some intermediate formalisms, the presented translation of LIO into ALBA is direct. As we expect applications of ALBA in model checking, we compare the expressiveness of ALBA with other classes of Buechi automata studied in this context and we indicate possible applications

Reasoning about transfinite sequences

We introduce a family of temporal logics to specify the behavior of systems with Zeno behaviors. We extend linear-time temporal logic LTL to authorize models admitting Zeno sequences of actions and quantitative temporal operators indexed by ordinals replace the standard next-time and until future-time operators. Our aim is to control such systems by designing controllers that safely work on $\omega$-sequences but interact synchronously with the system in order to restrict their behaviors. We show that the satisfiability problem for the logics working on $\omega^k$-sequences is EXPSPACE-complete when the integers are represented in binary, and PSPACE-complete with a unary representation. To do so, we substantially extend standard results about LTL by introducing a new class of succinct ordinal automata that can encode the interaction between the different quantitative temporal operators.Comment: 38 page

"More Deterministic" vs. "Smaller" Buechi Automata for Efficient LTL Model Checking

The standard technique for LTL model checking (M\models\neg\vi) consists on translating the negation of the LTL specification, \vi, into a B\"uchi automaton A_\vi, and then on checking if the product M \times A_\vi has an empty language. The efforts to maximize the efficiency of this process have so far concentrated on developing translation algorithms producing B\"uchi automata which are ``{\em as small as possible}'', under the implicit conjecture that this fact should make the final product smaller. In this paper we build on a different conjecture and present an alternative approach in which we generate instead B\"uchi automata which are ``{\em as deterministic as possible}'', in the sense that we try to reduce as much as we are able to the presence of non-deterministic decision states in A_\vi. We motivate our choice and present some empirical tests to support this approach

Ordered Navigation on Multi-attributed Data Words

We study temporal logics and automata on multi-attributed data words. Recently, BD-LTL was introduced as a temporal logic on data words extending LTL by navigation along positions of single data values. As allowing for navigation wrt. tuples of data values renders the logic undecidable, we introduce ND-LTL, an extension of BD-LTL by a restricted form of tuple-navigation. While complete ND-LTL is still undecidable, the two natural fragments allowing for either future or past navigation along data values are shown to be Ackermann-hard, yet decidability is obtained by reduction to nested multi-counter systems. To this end, we introduce and study nested variants of data automata as an intermediate model simplifying the constructions. To complement these results we show that imposing the same restrictions on BD-LTL yields two 2ExpSpace-complete fragments while satisfiability for the full logic is known to be as hard as reachability in Petri nets

On the Complexity of Temporal-Logic Path Checking

Given a formula in a temporal logic such as LTL or MTL, a fundamental problem is the complexity of evaluating the formula on a given finite word. For LTL, the complexity of this task was recently shown to be in NC. In this paper, we present an NC algorithm for MTL, a quantitative (or metric) extension of LTL, and give an NCC algorithm for UTL, the unary fragment of LTL. At the time of writing, MTL is the most expressive logic with an NC path-checking algorithm, and UTL is the most expressive fragment of LTL with a more efficient path-checking algorithm than for full LTL (subject to standard complexity-theoretic assumptions). We then establish a connection between LTL path checking and planar circuits, which we exploit to show that any further progress in determining the precise complexity of LTL path checking would immediately entail more efficient evaluation algorithms than are known for a certain class of planar circuits. The connection further implies that the complexity of LTL path checking depends on the Boolean connectives allowed: adding Boolean exclusive or yields a temporal logic with P-complete path-checking problem