Model Checking

Model checking of linear temporal logic (LTL) specifications with respect to pushdown systems has been shown to be a useful tool for analysis of programs with potentially recursive procedures. LTL, however, can specify only regular properties, and properties such as correctness of procedures with respect to pre and post conditions, that require matching of calls and returns, are not regular. We introduce a temporal logic of calls and returns (CaRet) for specification and algorithmic verification of correctness requirements of structured programs. The formulas of CaRet are interpreted over sequences of propositional valuations tagged with special symbols call and ret. Besides the standard global temporal modalities, CaRet admits the abstract-next operator that allows a path to jump from a call to the matching return. This operator can be used to specify a variety of non-regular properties such as partial and total correctness of program blocks with respect to pre and post conditions. The abstract versions of the other temporal modalities can be used to specify regular properties of local paths within a procedure that skip over calls to other procedures. CaRet also admits the caller modality that jumps to the most recent pending call, and such caller modalities allow specification of a variety of security properties that involve inspection of the call-stack. Even though verifying context-free properties of pushdown systems is undecidable, we show that model checking CaRet formulas against a pushdown model is decidable. We present a tableau construction that reduces our model checking problem to the emptiness problem for a Buchi pushdown system. The complexity of model checking CaRet formulas is the same as that of checking LTL formulas, namely, polynomial in the model and singly exponential in the size of the specification.

https://repository.upenn.edu/cgi/viewcontent.cgi?article=1186&context=cis_papers

A Temporal Logic of Nested Calls and Returns

Publisher Summary This chapter discusses temporal and modal logic. The chapter describes a multiaxis classification of systems of temporal logic. The chapter describes the framework of linear temporal logic. In both its propositional and first-order forms, linear temporal logic has been widely employed in the specification and verification of programs. The chapter describes the competing framework of branching temporal logic, which has seen wide use. It also explains how temporal logic structures can be used to model concurrent programs using non-determinism and fairness. The chapter also discusses other modal and temporal logics in computer science. The chapter describes the formal syntax and semantics of Propositional Linear Temporal Logic (PLTL). The chapter also describes the formal syntax and semantics for two representative systems of propositional branching-time temporal logics.

Temporal and modal logic

A type system is a syntactic method for automatically checking the absence of certain erroneous behaviors by classifying program phrases according to the kinds of values they compute. The study of type systems -- and of programming languages from a type-theoretic perspective -- has important applications in software engineering, language design, high-performance compilers, and security.This text provides a comprehensive introduction both to type systems in computer science and to the basic theory of programming languages. The approach is pragmatic and operational; each new concept is motivated by programming examples and the more theoretical sections are driven by the needs of implementations. Each chapter is accompanied by numerous exercises and solutions, as well as a running implementation, available via the Web. Dependencies between chapters are explicitly identified, allowing readers to choose a variety of paths through the material.The core topics include the untyped lambda-calculus, simple type systems, type reconstruction, universal and existential polymorphism, subtyping, bounded quantification, recursive types, kinds, and type operators. Extended case studies develop a variety of approaches to modeling the features of object-oriented languages.

https://www.seas.upenn.edu/~bcpierce/tapl/contents.pdf

Types and Programming Languages

In joint work with Peter O'Hearn and others, based on early ideas of Burstall, we have developed an extension of Hoare logic that permits reasoning about low-level imperative programs that use shared mutable data structure. The simple imperative programming language is extended with commands (not expressions) for accessing and modifying shared structures, and for explicit allocation and deallocation of storage. Assertions are extended by introducing a "separating conjunction" that asserts that its subformulas hold for disjoint parts of the heap, and a closely related "separating implication". Coupled with the inductive definition of predicates on abstract data structures, this extension permits the concise and flexible description of structures with controlled sharing. In this paper, we survey the current development of this program logic, including extensions that permit unrestricted address arithmetic, dynamically allocated arrays, and recursive procedures. We also discuss promising future directions.

/pdf/separation-logic-a-logic-for-shared-mutable-data-structures-1oyj7ddi1a.pdf

Separation logic: a logic for shared mutable data structures

From the Publisher:
Among the many approaches to formal reasoning about programs, Dynamic Logic enjoys the singular advantage of being strongly related to classical logic. Its variants constitute natural generalizations and extensions of classical formalisms. For example, Propositional Dynamic Logic (PDL) can be described as a blend of three complementary classical ingredients: propositional calculus, modal logic, and the algebra of regular events. In First-Order Dynamic Logic (DL), the propositional calculus is replaced by classical first-order predicate calculus. Dynamic Logic is a system of remarkable unity that is theoretically rich as well as of practical value. It can be used for formalizing correctness specifications and proving rigorously that those specifications are met by a particular program. Other uses include determining the equivalence of programs, comparing the expressive power of various programming constructs, and synthesizing programs from specifications. 
This book provides the first comprehensive introduction to Dynamic Logic. It is divided into three parts. The first part reviews the appropriate fundamental concepts of logic and computability theory and can stand alone as an introduction to these topics. The second part discusses PDL and its variants, and the third part discusses DL and its variants. Examples are provided throughout, and exercises and a short historical section are included at the end of each chapter.

Dynamic Logic

Publisher Summary This chapter presents an introduction to some of the basic issues in the study of program logics. The chapter describes various forms of first-order Dynamic Logic and discusses their syntax, semantics, proof theory, and expressiveness. The chapter discusses the power of auxiliary data structures such as arrays and stacks, and a powerful assignment statement called the nondeterministic assignment. Program logics differ from classical logics in that truth is dynamic rather than static. In classical predicate logic, the truth value of a formula is determined by a valuation of its free variables over some structure. The valuation and the truth value of the formula it induces are regarded as immutable. In program logics, there are explicit syntactic constructs called programs to change the values of variables, thereby changing the truth values of formulas. There are two main approaches to modal logics of programs: (1) the exogenous approach, exemplified by Dynamic Logic and its precursor, the Partial Correctness Assertions Method; and (2) the endogenous approach, exemplified by Temporal Logic and its precursor, the Inductive Assertions Method.

Logics of Programs.

A central goal of molecular biology is to understand the regulatory mechanisms of gene transcription and protein synthesis. Because of their solid basis in statistics, allowing to deal with the stochastic aspects of gene expressions and noisy measurements in a natural way, Bayesian networks appear attractive in the field of inferring gene interactions structure from microarray experiments data. However, the basic formalism has some disadvantages, e.g. it is sometimes hard to distinguish between the origin and the target of an interaction. Two kinds of microarray experiments yield data particularly rich in information regarding the direction of interactions: time series and perturbation experiments. In order to correctly handle them, the basic formalism must be modified. For example, dynamic Bayesian networks (DBN) apply to time series microarray data. To our knowledge the DBN technique has not been applied in the context of perturbation experiments. We extend the framework of dynamic Bayesian networks in order to incorporate perturbations. Moreover, an exact algorithm for inferring an optimal network is proposed and a discretization method specialized for time series data from perturbation experiments is introduced. We apply our procedure to realistic simulations data. The results are compared with those obtained by standard DBN learning techniques. Moreover, the advantages of using exact learning algorithm instead of heuristic methods are analyzed. We show that the quality of inferred networks dramatically improves when using data from perturbation experiments. We also conclude that the exact algorithm should be used when it is possible, i.e. when considered set of genes is small enough.

/pdf/applying-dynamic-bayesian-networks-to-perturbed-gene-2id3abqafj.pdf

Jerzy Tiuryn

Papers

Dynamic Logic

Logics of Programs.

Applying dynamic Bayesian networks to perturbed gene expression data.

DLS-trees: a model of evolutionary scenarios

Logics of programs