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.

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.

scholarly journals On Computational Tractability for Rational Verification

2019 ◽  
Author(s):  
Julian Gutierrez ◽  
Muhammad Najib ◽  
Giuseppe Perelli ◽  
Michael Wooldridge
Keyword(s):  
Model Checking ◽  
Temporal Logic ◽  
Multiagent Systems ◽  
Polynomial Time ◽  
Multiagent System ◽  
Reactive Systems ◽  
State System ◽  
Polynomial Space ◽  
Game Theoretic ◽  
Mean Payoff

Rational verification involves checking which temporal logic properties hold of a concurrent and multiagent system, under the assumption that agents in the system choose strategies in game theoretic equilibrium. Rational verification can be understood as a counterpart of model checking for multiagent systems, but while model checking can be done in polynomial time for some temporal logic specification languages such as CTL, and polynomial space with LTL specifications, rational verification is much more intractable: it is 2EXPTIME-complete with LTL specifications, even when using explicit-state system representations.  In this paper we show that the complexity of rational verification can be greatly reduced by restricting specifications to GR(1), a fragment of LTL that can represent most response properties of reactive systems. We also provide improved complexity results for rational verification when considering players' goals given by mean-payoff utility functions -- arguably the most widely used quantitative objective for agents in concurrent and multiagent systems. In particular, we show that for a number of relevant settings, rational verification can be done in polynomial space or even in polynomial time.

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.

Modeling security properties of authentication of cryptographic protocols using spin formal verification

2020 ◽  
pp. 21-25
Author(s):  
E.A. Perevyshina ◽  
L.K. Babenko
Keyword(s):  
Model Checking ◽  
Formal Verification ◽  
Temporal Logic ◽  
Cryptographic Protocols ◽  
Wide Range ◽  
Security Properties ◽  
Verification Tools ◽  
The Stability ◽  
Security Property ◽  
Ltl Model Checking

To assess the quality and security of cryptographic protocols, we use various formal verification tools, such as Scyther tool, Avispa, ProVerif. these formal verifiers can check the protocol for vulnerability to attacks on secrecy and authentication, as these are the most prevalent attacks on protocols. However, this is not enough to fully analyze the security of the protocol. In this article, we will use linear temporal logic (LTL) model checking with SPIN. This tool, unlike the formal verifiers listed above, is not designed for a specific application in the context of cryptographic protocols; however, it has a very wide range of possibilities. In particular, for each security property, it is possible to describe the behavior of an attacker and test for the stability of the protocol model to its various attacks. The purpose of this work is to describe the developed methodology for verifying the security of authentication properties using the SPIN verifier.

Logical foundations of hierarchical model checking

2018 ◽  
Vol 52 (4) ◽  
pp. 539-563 ◽  
Author(s):  
Norihiro Kamide
Keyword(s):  
Model Checking ◽  
Temporal Logic ◽  
Hierarchical Model ◽  
Design Methodology ◽  
Linear Time ◽  
Hierarchical Systems ◽  
Content Type ◽  
Computation Tree Logic ◽  
Computation Tree ◽  
Linear Time Temporal Logic

Purpose The purpose of this paper is to develop new simple logics and translations for hierarchical model checking. Hierarchical model checking is a model-checking paradigm that can appropriately verify systems with hierarchical information and structures. Design/methodology/approach In this study, logics and translations for hierarchical model checking are developed based on linear-time temporal logic (LTL), computation-tree logic (CTL) and full computation-tree logic (CTL*). A sequential linear-time temporal logic (sLTL), a sequential computation-tree logic (sCTL), and a sequential full computation-tree logic (sCTL*), which can suitably represent hierarchical information and structures, are developed by extending LTL, CTL and CTL*, respectively. Translations from sLTL, sCTL and sCTL* into LTL, CTL and CTL*, respectively, are defined, and theorems for embedding sLTL, sCTL and sCTL* into LTL, CTL and CTL*, respectively, are proved using these translations. Findings These embedding theorems allow us to reuse the standard LTL-, CTL-, and CTL*-based model-checking algorithms to verify hierarchical systems that are modeled and specified by sLTL, sCTL and sCTL*. Originality/value The new logics sLTL, sCTL and sCTL* and their translations are developed, and some illustrative examples of hierarchical model checking are presented based on these logics and translations.

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