Extension Of Computation Tree Logic Research Articles

Towards Combining Model Checking and Proof Checking

Model checking and automated theorem proving are two pillars of formal verification methods. This paper investigates model checking from an automated theorem proving perspective, aiming at combining the expressiveness of automated theorem proving and the complete automaticity of model checking. It places the focus on the verification of temporal logic properties of Kripke models. The main contributions are: (1) introducing an extended computation tree logic that allows polyadic predicate symbols; (2) designing a proof system for this logic, taking Kripke models as parameters; (3) developing a proof search algorithm for this system and a new automated theorem prover to implement it. The verification process of the new prover is completely automatic, and produces either a counterexample when the property does not hold, or a certificate when it does. The experimental results compare well to existing state-of-the-art tools on some benchmarks, and the efficiency is illustrated by application to an air traffic control problem.

Probabilistic regular graphs

Deterministic graph grammars generate regular graphs, that form a structural extension of configuration graphs of pushdown systems. In this paper, we study a probabilistic extension of regular graphs obtained by labelling the terminal arcs of the graph grammars by probabilities. Stochastic properties of these graphs are expressed using PCTL, a probabilistic extension of computation tree logic. We present here an algorithm to perform approximate verification of PCTL formulae. Moreover, we prove that the exact model-checking problem for PCTL on probabilistic regular graphs is undecidable, unless restricting to qualitative properties. Our results generalise those of EKM06, on probabilistic pushdown automata, using similar methods combined with graph grammars techniques.

CTL-RP: A computation tree logic resolution prover

In this paper, we present a resolution-based calculus R CTL >,S for Computation Tree Logic (CTL) as well as an implementation of that calculus in the theorem prover CTL-RP. The calculus R CTL >,S requires a transformation of an arbitrary CTL formula to an equi-satisfiable clausal normal form formulated in an extension of CTL with indexed path formulae. The calculus itself consists of a set of resolution rules which can be used for an EXPTIME decision procedure for the satisfiability problem of CTL. We give a formal semantics for the clausal normal form, provide proof sketches for the soundness and completeness of the resolution rules, discuss the complexity of the decision procedure based on R CTL >,S, and present an approach to implementing the calculus R CTL >,S using first-order techniques. Finally, we give a comparison between CTL-RP and a tableau theorem prover for CTL.

Superior induction of anti‐tumor CTL immunity by extended peptide vaccines involves prolonged, DC‐focused antigen presentation

Anti-tumor vaccines consisting of extended CTL peptides in combination with CpG-ODN were shown to be superior to those comprising minimal CTL epitopes and CpG-ODN, in that they elicit stronger effector CTL responses with greater tumoricidal potential. We now demonstrate that this improved performance is primarily due to the focusing of CTL epitope presentation onto activated DC in the inflamed lymph nodes draining the vaccination site. In the case of vaccination with minimal peptides, additional APC including T and B cells are also loaded with CTL epitopes. Our data suggest that circulation of these peptide-loaded lymphocytes leads to epitope presentation in non-inflamed lymphoid organs distal from the vaccination site, in the absence of potent costimulatory signals required for efficient CTL priming. The resulting blend of pro-immunogenic and tolerogenic signals, which results in suboptimal activation of the CTL response, is avoided by vaccinating with extended CTL peptides. An additional advantage of extended CTL peptide vaccines is an increased duration of in vivo epitope presentation.

Checking extended CTL properties using guarded quotient structures

We extend CTL logic to a logic called COUNT CTL (CCTL) for specifying properties of concurrent programs with large number of processes. We present a model checking algorithm for symmetric or partially symmetric systems when their correctness specification is given in CCTL. The model-checking algorithm employs Guarded Quotient Structures introduced by Sistla and Godefroid (Lecture Notes in Comput. Sci., vol. 2102, 2001). The GQS structures can be succinct representations for the reachability graphs of partially symmetric or even asymmetric systems. Our algorithm exploits state symmetries for fast evaluation. The algorithm is top down in nature, and automatically incorporates formula decomposition and sub-formula tracking.

A clausal resolution method for extended computation tree logic ECTL

A temporal clausal resolution method was originally developed for linear time temporal logic and further extended to the branching-time framework of Computation Tree Logic (CTL). In this paper, following our general idea to expand the applicability of this efficient method to more expressive formalisms useful in a variety of applications in computer science and AI requiring branching time logics, we define a clausal resolution technique for Extended Computation Tree Logic (ECTL). The branching-time temporal logic ECTL is strictly more expressive than CTL in allowing fairness operators. The key elements of the resolution method for ECTL, namely the clausal normal form, the concepts of step resolution and a temporal resolution, are introduced and justified with respect to this new framework. Although in developing these components we incorporate many of the techniques defined for CTL, we need novel mechanisms in order to capture fairness together with the limit closure property of the underlying tree models. We accompany our presentation of the relevant techniques by examples of the application of the temporal resolution method. Finally, we provide a correctness argument and consider future work discussing an extension of the method yet further, to the logic CTL ∗, the most powerful logic of this class.

The open family of temporal logics

Assume-guarantee style verification of modules relies on the appropriate modeling of the interaction of the module with its environment. Popular temporal logics such as Computation Tree Logic (CTL) and Linear Temporal Logic (LTL) that were originally defined for closed systems (Kripke structures) do not make any syntactic discrimination between input and output variables. As a result, these logics and their recent derivatives (such as System Verilog, Sugar, Forspec, etc) permit the specification of properties that have some semantic problems when interpreted over open systems or modules. These semantic problems are quite common in practice, but are computationally hard to detect within a given specification. In this article, we propose a new style for writing temporal specifications of open systems that helps the designer to avoid most of these problems. In the proposed style, the basic temporal operators (such as next and until ) are annotated with assume constraints over the input variables. We formalize this style through an extension of LTL, namely Open-LTL and an extension of CTL with fairness, called Open-CTL. We show that this simple syntactic separation between the assume and the guarantee achieves the desired results. We show that the proposed style can be integrated with traditional symbolic model-checking techniques and present a complete tool for the verification of Verilog RTL modules in isolation.

A Branching Time Temporal Framework for Quantitative Reasoning

Temporal logics such as Computation Tree Logic (CTL) and Linear Temporal Logic (LTL) have become popular for specifying temporal properties over a wide variety of planning and verification problems. In this paper we work towards building a generalized framework for automated reasoning based on temporal logics. We present a powerful extension of CTL with first-order quantification over the set of reachable states for reasoning about extremal properties of weighted labeled transition systems in general. The proposed logic, which we call Weighted Quantified Computation Tree Logic (WQCTL), captures the essential elements common to the domain of planning and verification problems and can thereby be used as an effective specification language in both domains. We show that in spite of the rich, expressive power of the logic, we are able to evaluate WQCTL formulas in time polynomial in the size of the state space times the length of the formula. We present experimental results on the WQCTL verifier.

A clausal resolution method for CTL branching-time temporal logic

In this paper we extend our clausal resolution method for linear time temporal logics to a branching-time framework. Thus, we propose an efficient deductive method useful in a variety of applications requiring an expressive branching-time temporal logic in AI. The branching-time temporal logic considered is Computation Tree Logic (CTL), often regarded as the simplest useful logic of this class. The key elements of the resolution method, namely the normal form, the concept of step resolution and a novel temporal resolution rule, are introduced and justified with respect to this logic. A completeness argument is provided, together with some examples of the use of the temporal resolution method. Finally, we consider future work, in particular the extension of the method yet further, to Extended CTL (ECTL), which is CTL extended with fairness operators, and CTL*, the most powerful logic of this class. We will also outline possible implementation of the approach by adapting techniques developed for linear-time temporal resolution.

Axiomatising extended computation tree logic

We present a sound and complete axiomatisation for extended computation tree logic. This language extends the standard computation tree logic CTL ∗ by allowing path formulae to be expressed in linear time mu-calculus instead of linear-time temporal logic. The main novelties in the current paper are an inference rule in the axiom system reflecting the limit closure of paths, a new strongly aconjunctive deterministic normal form for formulae, and the way the completeness proof takes advantage of techniques provided by automata theory.

TEMPORAL LOGICS FOR TRACE SYSTEMS: ON AUTOMATED VERIFICATION

We investigate an extension of CTL (Computation Tree Logic) by past modalities, called CTL P, interpreted over Mazurkiewicz’s trace systems. The logic is powerful enough to express most of the partial order properties of distributed systems like serializability of database transactions, snapshots, parallel execution of program segments, or inevitability under concurrency fairness assumption. We show that the model checking problem for the logic is NP-hard, even if past modalities cannot be nested. Then, we give a one exponential time model checking algorithm for the logic without nested past modalities. We show that all the interesting partial order properties can be model checked using our algorithm. Next, we show that is is possible to extend the model checking algorithm to cover the whole language and its extension to [Formula: see text]. Finally, we prove that the logic is undecidable and we discuss consequences of our results on using propositional versions of partial order temporal logics to synthesis of concurrent systems from their specifications.