scholarly journals A Weakness Measure for GR(1) Formulae

2020 ◽  
Author(s):  
Davide G. Cavezza ◽  
Dalal Alrajeh ◽  
András György
Keyword(s):  
Hausdorff Dimension ◽  
Model Checking ◽  
Temporal Logic ◽  
Linear Temporal Logic ◽  
Quantitative Model ◽  
Reactive Synthesis ◽  
Logic Formula ◽  
Special Subset ◽  
Temporal Logic Formula ◽  
Insight Into

Abstract When dealing with unrealizable specifications in reactive synthesis, finding the weakest environment assumptions that ensure realizability is often considered a desirable property. However, little effort has been dedicated to defining or evaluating the notion of weakness of assumptions formally. The question of whether one assumption is weaker than another is commonly interpreted by considering the implication relationship between the two or, equivalently, their language inclusion. This interpretation fails to provide any insight into the weakness of the assumptions when implication (or language inclusion) does not hold. To our knowledge, the only measure that is capable of comparing two formulae in this case is entropy, but even it cannot distinguish the weakness of assumptions expressed as fairness properties. In this paper, we propose a refined measure of weakness based on combining entropy with Hausdorff dimension, a concept that captures the notion of size of the $$\omega $$ ω -language satisfying a linear temporal logic formula. We focus on a special subset of linear temporal logic formulae which is of particular interest in reactive synthesis, called GR(1). We identify the conditions under which this measure is guaranteed to distinguish between weaker and stronger GR(1) formulae, and propose a refined measure to cover cases when two formulae are strictly ordered by implication but have the same entropy and Hausdorff dimension. We prove the consistency between our weakness measure and logical implication, that is, if one formula implies another, the latter is weaker than the former according to our measure. We evaluate our proposed weakness measure in two contexts. The first is in computing GR(1) assumption refinements where our weakness measure is used as a heuristic to drive the refinement search towards weaker solutions. The second is in the context of quantitative model checking where it is used to measure the size of the language of a model violating a linear temporal logic formula.

Model Checking of Constraint-Based Workflow Based on Linear Temporal Logic

2012 ◽  
Vol 601 ◽  
pp. 401-405
Author(s):  
Wen Bo Zhou ◽  
Shu Zhen Yao
Keyword(s):  
Model Checking ◽  
Temporal Logic ◽  
Business Processes ◽  
Workflow Management ◽  
Linear Temporal Logic ◽  
Management Systems ◽  
Workflow Management Systems ◽  
Model Based ◽  
Büchi Automaton ◽  
Constraint Based Models

The degree of flexibility of workflow management systems heavily influences the way business processes are executed. Constraint-based models are considered to be more flexible than traditional models because of their semantics: everything that does not violate constraints is allowed. More and more people use declarative languages to define workflow, such as linear temporal logic. But how to guarantee the correctness of the model based on the linear temporal logic is still a problem. This article proposes a way to verify the model based on Büchi automaton and gives the corresponding algorithms. Thus the verification of declarative workflow based on the linear temporal logic is solved.

scholarly journals Converging from branching to linear metrics on Markov chains

2017 ◽  
Vol 29 (1) ◽  
pp. 3-37 ◽  
Author(s):  
GIORGIO BACCI ◽  
GIOVANNI BACCI ◽  
KIM G. LARSEN ◽  
RADU MARDARE
Keyword(s):  
Model Checking ◽  
Markov Chains ◽  
Temporal Logic ◽  
Polynomial Time ◽  
Linear Time ◽  
Linear Temporal Logic ◽  
Np Hard ◽  
Branching Time ◽  
Threshold Problem ◽  
Ltl Model Checking

We study two well-known linear-time metrics on Markov chains (MCs), namely, the strong and strutter trace distances. Our interest in these metrics is motivated by their relation to the probabilistic linear temporal logic (LTL)-model checking problem: we prove that they correspond to the maximal differences in the probability of satisfying the same LTL and LTL−X(LTL without next operator) formulas, respectively.The threshold problem for these distances (whether their value exceeds a given threshold) is NP-hard and not known to be decidable. Nevertheless, we provide an approximation schema where each lower and upper approximant is computable in polynomial time in the size of the MC.The upper approximants are bisimilarity-like pseudometrics (hence, branching-time distances) that converge point-wise to the linear-time metrics. This convergence is interesting in itself, because it reveals a non-trivial relation between branching and linear-time metric-based semantics that does not hold in equivalence-based semantics.

scholarly journals BDD-versus SAT-based bounded model checking for the existential fragment of linear temporal logic with knowledge: algorithms and their performance

2013 ◽  
Vol 28 (4) ◽  
pp. 558-604 ◽  
Author(s):  
Artur Mȩski ◽  
Wojciech Penczek ◽  
Maciej Szreter ◽  
Bożena Woźna-Szcześniak ◽  
Andrzej Zbrzezny
Keyword(s):  
Model Checking ◽  
Temporal Logic ◽  
Linear Temporal Logic ◽  
Bounded Model Checking

A LOGIC BASED APPROACH TO PLANNING FOR SPECIFYING A CLASS OF TEMPORALLY EXTENDED GOALS

2004 ◽  
Vol 13 (03) ◽  
pp. 469-485 ◽  
Author(s):  
RAJDEEP NIYOGI
Keyword(s):  
Model Checking ◽  
Temporal Logic ◽  
Polynomial Time ◽  
Linear Temporal Logic ◽  
The Other ◽  
Logical Framework ◽  
Branching Time ◽  
Optimal Plan ◽  
Other Hand ◽  
Planning Procedure

Planning with temporally extended goals has recently been the focus of much attention to researchers in the planning community. We study a class of planning goals where in addition to a main goal there exist other goals, which we call auxiliary goals, that act as constraints to the main goal. Both these type of goals can, in general, be a temporally extended goal. Linear temporal logic (LTL) is inadequate for specification of the overall goals of this type, although, for some situations, it is capable of expressing them separately. A branching-time temporal logic, like CTL, on the other hand, can be used for specifying these goals. However, we are interested in situations where an auxiliary goal has to be satisfiable within a fixed bound. We show that CTL becomes inadequate for capturing these situations. We bring out an existing logic, called min-max CTL, and show how it can effectively be used for the planning purpose. We give a logical framework for expressing the overall planning goals. We propose a sound and complete planning procedure that incorporates a model checking technology. Doing so, we can answer such planning queries as plan existence at the onset besides producing an optimal plan (if any) in polynomial time.

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