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Register a new userEfficient Decentralized LTL Monitoring Framework Using Tableau Technique
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Added by
Omar Al-Bataineh I.
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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This paper presents a novel framework for decentralized monitoring of Linear Temporal Logic (LTL), under the situation where processes are synchronous, uniform (i.e. all processes are peers), and the formula is represented as a tableau. The tableau technique allows one to construct a semantic tree for the input formula, which can be used to optimize the decentralized monitoring of LTL in various ways. Given a system P and an LTL formula L, we construct a tableau for L. The tableauis used for two purposes: (a) to synthesize an efficient round-robin communication policy for processes, and (b) to allow processes to propagate their observations in an optimal way. In our framework, processes can propagate truth values of atomic formulas, compound formulas, and temporal formulas depending on the syntactic structure of the input LTL formula and the observation power of processes. We demonstrate that this approach of decentralized monitoring based on tableau construction is more straightforward, more flexible, and more likely to yield efficient solutions than alternative approaches.
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This paper presents a new technique for optimizing formal analysis of propositional logic formulas and Linear Temporal Logic (LTL) formulas, namely the formula simplification table. A formula simplification table is a mathematical table that shows all possible simplifications of the formula under different truth assignments of its variables. The advantages of constructing a simplification table of a formula are two-fold. First, it can be used to compute the logical influence weight of each variable in the formula, which is a metric that shows the importance of the variable in affecting the outcome of the formula. Second, it can be used to identify variables that have the highest logical influences on the outcome of the formula. %The simplification table can be used to optimize %existing solutions for several interesting %LTL verification problems. We demonstrate the effectiveness of formula simplification table in the context of software verification by developing efficient framework to the well-known decentralized LTL monitoring problem.
Propositional linear time temporal logic (LTL) is the standard temporal logic for computing applications and many reasoning techniques and tools have been developed for it. Tableaux for deciding satisfiability have existed since the 1980s. However, the tableaux for this logic do not look like traditional tree-shaped tableau systems and their processing is often quite complicated. We present a new simple traditional-style tree-shaped tableau for LTL and prove that it is sound and complete. As well as being simple to understand, to introduce to students and to use manually, it also seems simple to implement and promises to be competitive in its automation. It is particularly suitable for parallel implementations.
In recent years, there is growing need and interest in formalizing and reasoning about the quality of software and hardware systems. As opposed to traditional verification, where one handles the question of whether a system satisfies, or not, a given specification, reasoning about quality addresses the question of emph{how well} the system satisfies the specification. One direction in this effort is to refine the eventually operators of temporal logic to {em discounting operators}: the satisfaction value of a specification is a value in $[0,1]$, where the longer it takes to fulfill eventuality requirements, the smaller the satisfaction value is. In this paper we introduce an augmentation by discounting of Linear Temporal Logic (LTL), and study it, as well as its combination with propositional quality operators. We show that one can augment LTL with an arbitrary set of discounting functions, while preserving the decidability of the model-checking problem. Further augmenting the logic with unary propositional quality operators preserves decidability, whereas adding an average-operator makes some problems undecidable. We also discuss the complexity of the problem, as well as various extensions.
This continuously extended technical report collects and compares commonly used formulae from the literature and provides them in a machine readable way.
For many applications, we are unable to take full advantage of the potential massive parallelisation offered by supercomputers or cloud computing because it is too hard to work out how to divide up the computation task between processors in such a way to minimise the need for communication. However, a recently developed branch-independent tableaux for the common LTL temporal logic should intuitively be easy to parallelise as each branch can be developed independently. Here we describe a simple technique for partitioning such a tableau such that each partition can be processed independently without need for interprocess communication. We investigate the extent to which this technique improves the performance of the LTL tableau on standard benchmarks and random formulas.
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