Simply defined, a fault tree is a graphical representa tion of the logic that relates certain specific events or primary failures to an ultimate undesired event. In this lecture we will cover ctl, a logic to reason about sequence of events. Propositional temporal logic is not suitable for expressing properties on the evolution of dynamically allocated entities over time. Computation tree logic ctl is a branchingtime logic, meaning that its model of time is a treelike structure in which the future is not determined. In this expository paper, we make some of these analogies pre. The computation tree logic, ctl, solves these problems. Ctl computation tree logic, was first described in emerson and sistla, 1984 and emerson and halpern, 1986. In ctl, as well as the temporal operators x, f, g and u of ltl we also. To do this, we first recall the concept of kripke structure and some. Computation trees a finite state model m s, r, l and a state s 0. Besides classical propositional logic and firstorder predicate logic with functions, but without identity, a few normal modal logics are supported. Parse tree given a ctlformula we construct a parse tree s. In this paper, a paraconsistent computation tree logic, pctl, is obtained by adding paraconsistent negation to the standard computation tree logic ctl. If you enter a modal formula, you will see a choice of how the accessibility relation should be constrained.
A clausal resolution for extended computation tree logic. A comparison to ltl based on expressiveness is provided. Computation tree logic pnueli 88 has introduced linear temporal logic to the computer science community for the speci cation and veri cation of reactive systems. We present a logic that extends ctl computation tree logic with operators that express synchronization properties. In a linear temporal logic, operators are provided for describing events along a single computation path. This is used in two almost undistinguishable ways, we talk about finite computation trees, and we talk about computations in n steps. One important aspect of standard recursion theory is that any successful computation is finite. Boyer and j strother moore sri international menlo park, california academic press. Antonio gonz alez burgueno uio computation tree logic ctl may 26, 2017 5 29. Computation tree logic ctl is one of the most syntactically elegant and computationally attractive temporal logics for branching time model checking. It is known that paraconsistent logical systems are more appropriate for inconsistencytolerant and uncertainty reasoning than other types of logical systems. Pctl can be used to appropriately formalize inconsistencytolerant. This makes the logic a promising candidate for applications in veri. Pdf we study the equivalence relation on states of labelled transition systems of satisfying the same formulas in computation tree logic without the.
We prove soundness and completeness of hilbert systems and historybased gentzen systems, smallmodel theorems, and decidability results. Ctl is the natural temporal logic interpreted over branching time structures. Computation tree logics temporal logics may differ according to how they handle branching in the underlying computation tree. Computational tree logic propositional branching time logic, permitting explicit quantification over all possible futures. Computation tree logic ctl and path quantifiers in the. In a temporal logic, an atom is no longer always true or always false. Definition of computation tree logic in the dictionary. Quantitative computation tree logic model checking based on. In reliability and systems analysis, a fault tree analysis has many uses. Theory of computation and automata tutorials geeksforgeeks.
Computation tree logic ctl is one of the main logical formalisms for program. The chapter concludes with an extension called ctl which subsumes both ctl and ltl. It is able to handle both sequential and parallel composition. The journal of symbolic logic volume 66, number 3, sept. A list of lyrics, artists and songs that contain the term computation tree logic from the website.
Furthermore, to enable practical vulnerability checking, we present a new approach that limits the depth of the execution paths that need to be checked by the computation tree logic, allowing for use of bounded model checking for computation tree logic based cache security verification using the new threestep singlecacheblockaccess model. Introduction to formal verification donald pederson. Pdf quantified computation tree logic anindya c patthak. Interval temporal logic itl 2, 3 represents both propositional and. And i like to switch between a modeling formalism and the logic you can use for model checking. Linear temporal logic is a very important logic for model checking eme90,cgp99, bkl08 but has the downside that its veri. Pctl can be used to appropriately formalize inconsistencytolerant temporal reasoning. T contains an edge from a node labeled s to a node labeled t iff s, t. It has been defined in the paper by hansson and jonsson. A temporal clausal resolution method was originally developed for linear time temporal logic and further extended to the branchingtime framework of computation tree logic ctl. Introduction to computation tree logic 1823 the model checking procedure. In particular, it is not possible to trace such entities through computation steps, since this requires the ability to freely mix quantification and temporal operators. For instance, we will write formally statements such as.
Computability and complexity theory is, and should be, of central concern for practitioners as well as theorists. Computation tree logic for synchronization properties lsv. In this section we introduce and discuss the syntax and semantics of cyclectl. In chapter 3 we have treated one important kind of linear temporal logic, called pltl. By using a slightly unusual semantics based on paths through transition. This temporal logic is called linear, because the qualitative notion of time. R a ctl formula is evaluated on a computation tree. Introduction linear time properties regular properties. Cache timing sidechannel vulnerability checking with.
A machinechecked constructive metatheory of computation. Design and synthesis of synchronisation skeletons using branching time temporal logic pdf. When we work with computations where the input is a list of. In a branchingtime logic the temporal operators quantify over the paths that are possible from a given state.
Quantitative computation tree logic model checking based on generalized possibility measures yongming li. A ctl formula is evaluated on a computation tree, i. Computation trees are derived from state transition graphs. Formulas of extended computation tree logic over 2 and 3 ctl2,3 are given by the. From any state it is possible to get to the restart state. Srivathsan chennai mathematical institute model checking and systems veri. The main languages here are the purely branching computational tree logic ctl and the combined branchinglinear full computational tree logic ctl. Information and translations of computation tree logic in the most comprehensive dictionary definitions resource on the web. Computation tree logic hao zheng department of computer science and engineering university of south florida tampa, fl 33620 email. This thesis presents a machinechecked constructive metatheory of computation tree logic ctl and its sublogics k and k based on results from the literature.
So in this first module well deal with computational tree logic, and computational tree logic can be used to model check labeled transition systems. With the rise of interest in quantum cryptography and quantum computation, it became clear that there is extensive network of analogies between physics, topology, logic and computation. This first lecture is meant as an introduction to the subject. Rather than trying to model or simulate attackers, this work explic. In this paper, following our general idea to expand the applicability of this efficient method to more expressive. Computation tree logic ctl is a branchingtime logic, meaning that its model of time is a tree like structure in which the future is not determined. In particular, properties which mix existential and universal path quanti. It is used in formal verification of software or hardware artifacts, typically by software applications known as model checkers which determine if. Computation tree logic mickael randour mathematics department, umons october 2019. Guerra and renata wassermann university of sao paulo. A computational logic acm monographs series includes bibliographic references and index. Probabilistic computation tree logic pctl is an extension of computation tree logic ctl which allows for probabilistic quantification of described properties.
Extended computation tree logic roland axelsson1, matthew hague2, stephan kreutzer2, martin lange3, and markus latte1 1 department of computer science, ludwigmaximiliansuniversit. There exists an execution of the system such that, if the proposition p is true, then in the next computation step qis true. Computation tree logic ctl is a branchingtime logic, meaning that its model of time is a. Computation tree logic ctl 15 is a superset of computation tree logic ctl and linear temporal logic ltl.
It is shown that matching mu logic captures as special instances many important logics in mathematics and computer science, including firstorder logic with least fixpoints, modal mu logic as well as dynamic logic and various temporal logics such as infinitefinitetrace linear temporal logic and computation tree logic, and notably reachability. We introduce computation tree logic ctl, a branching temporal logic for specifying system properties. A comparison to ltl based on expressiveness 2 is provided. The computation tree logicctl solves these problems. Nov 10, 2011 it is known that paraconsistent logical systems are more appropriate for inconsistencytolerant and uncertainty reasoning than other types of logical systems. Quantitative computation tree logic model checking based. To get a good sense of how model checking works, we, thus, consider the closely related but different. We should exploit the duality of existential and universal quantification. Temporal logic flavors linear temporal logic ltl computation tree logic ctl, ctl properties expressed over a tree of all possible executions ctl gives more expressiveness than ltl ctl is a subset of ctl that is easier to verify than arbitrary ctl. The graph structure is unwound into an in nite tree rooted at the initial state.
Dag normann, in studies in logic and the foundations of mathematics, 1999. Srivathsan chennai mathematical institute nptelcourse july november 2015 5. Computation tree logic ctl and path quantifiers in the monadic theory of the binary tree. Pctl is a useful logic for stating soft deadline properties, e. Computation tree logic computational tree logic propositional branching time logic, permitting explicit quanti. In this logic a path quantifier can prefix an assertion composed of. The computation tree logic ctl combines both branchingtime and lineartime operators. Properties that assert the existence of a path cannot be expressed. Cycle detection in computation tree logic sciencedirect. Last minute noteslmns quizzes on theory of computation. R a ctl formula is evaluated on a computation tree, i.