Model Checking Synchronized Products of Infinite Transition Systems

Formal verification using the model checking paradigm has to deal with two aspects: The system models are structured, often as products of components, and the specification logic has to be expressive enough to allow the formalization of reachability properties. The present paper is a study on what can be achieved for infinite transition systems under these premises. As models we consider products of infinite transition systems with different synchronization constraints. We introduce finitely synchronized transition systems, i.e. product systems which contain only finitely many (parameterized) synchronized transitions, and show that the decidability of FO(R), first-order logic extended by reachability predicates, of the product system can be reduced to the decidability of FO(R) of the components. This result is optimal in the following sense: (1) If we allow semifinite synchronization, i.e. just in one component infinitely many transitions are synchronized, the FO(R)-theory of the product system is in general undecidable. (2) We cannot extend the expressive power of the logic under consideration. Already a weak extension of first-order logic with transitive closure, where we restrict the transitive closure operators to arity one and nesting depth two, is undecidable for an asynchronous (and hence finitely synchronized) product, namely for the infinite grid.Comment: 18 page

Linearly bounded infinite graphs

Linearly bounded Turing machines have been mainly studied as acceptors for context-sensitive languages. We define a natural class of infinite automata representing their observable computational behavior, called linearly bounded graphs. These automata naturally accept the same languages as the linearly bounded machines defining them. We present some of their structural properties as well as alternative characterizations in terms of rewriting systems and context-sensitive transductions. Finally, we compare these graphs to rational graphs, which are another class of automata accepting the context-sensitive languages, and prove that in the bounded-degree case, rational graphs are a strict sub-class of linearly bounded graphs

Behavioural Types: from Theory to Tools

This book presents research produced by members of COST Action IC1201: Behavioural Types for Reliable Large-Scale Software Systems (BETTY), a European research network that was funded from October 2012 to October 2016. The technical theme of BETTY was the use of behavioural type systems in programming languages, to specify and verify properties of programs beyond the traditional use of type systems to describe data processing. A significant area within behavioural types is session types, which concerns the use of type-theoretic techniques to describe communication protocols so that static typechecking or dynamic monitoring can verify that protocols are implemented correctly. This is closely related to the topic of choreography, in which system design starts from a description of the overall communication flows. Another area is behavioural contracts, which describe the obligations of interacting agents in a way that enables blame to be attributed to the agent responsible for failed interaction. Type-theoretic techniques can also be used to analyse potential deadlocks due to cyclic dependencies between inter-process interactions. BETTY was organised into four Working Groups: (1) Foundations; (2) Security; (3) Programming Languages; (4) Tools and Applications. Working Groups 1–3 produced “state-of-the-art reports”, which originally intended to take snapshots of the field at the time the network started, but grew into substantial survey articles including much research carried out during the network [1–3]. The situation for Working Group 4 was different. When the network started, the community had produced relatively few implementations of programming languages or tools. One of the aims of the network was to encourage more implementation work, and this was a great success. The community as a whole has developed a greater interest in putting theoretical ideas into practice. The sixteen chapters in this book describe systems that were either completely developed, or substantially extended, during BETTY. The total of 41 co-authors represents a significant proportion of the active participants in the network (around 120 people who attended at least one meeting). The book is a report on the new state of the art created by BETTY in xv xvi Preface the area of Working Group 4, and the title “Behavioural Types: from Theory to Tools” summarises the trajectory of the community during the last four years. The book begins with two tutorials by Atzei et al. on contract-oriented design of distributed systems. Chapter 1 introduces the CO2 contract specifi- cation language and the Diogenes toolchain. Chapter 2 describes how timing constraints can be incorporated into the framework and checked with the CO2 middleware. Part of the CO2 middleware is a monitoring system, and the theme of monitoring continues in the next two chapters. In Chapter 3, Attard et al. present detectEr, a runtime monitoring tool for Erlang programs that allows correctness properties to be expressed in Hennessy-Milner logic. In Chapter 4, which is the first chapter about session types, Neykova and Yoshida describe a runtime verification framework for Python programs. Communication protocols are specified in the Scribble language, which is based on multiparty session types. The next three chapters deal with choreographic programming. In Chap- ter 5, Debois and Hildebrandt present a toolset for working with dynamic condition response (DCR) graphs, which are a graphical formalism for choreography. Chapter 6, by Lange et al., continues the graphical theme with ChorGram, a tool for synthesising global graphical choreographies from collections of communicating finite-state automata. Giallorenzo et al., in Chapter 7, consider runtime adaptation. They describe AIOCJ, a choreographic programming language in which runtime adaptation is supported with a guarantee that it doesn’t introduce deadlocks or races. Deadlock analysis is important in other settings too, and there are two more chapters about it. In Chapter 8, Padovani describes the Hypha tool, which uses a type-based approach to check deadlock-freedom and lock-freedom of systems modelled in a form of pi-calculus. In Chapter 9, Garcia and Laneve present a tool for analysing deadlocks in Java programs; this tool, called JaDA, is based on a behavioural type system. The next three chapters report on projects that have added session types to functional programming languages in order to support typechecking of communication-based code. In Chapter 10, Orchard and Yoshida describe an implementation of session types in Haskell, and survey several approaches to typechecking the linearity conditions required for safe session implemen- tation. In Chapter 11, Melgratti and Padovani describe an implementation of session types in OCaml. Their system uses runtime linearity checking. In Chapter 12, Lindley and Morris describe an extension of the web programming language Links with session types; their work contrasts with the previous two chapters in being less constrained by an existing language design. Continuing the theme of session types in programming languages, the next two chapters describe two approaches based on Java. Hu’s work, presented in Chapter 13, starts with the Scribble description of a multiparty session type and generates an API in the form of a collection of Java classes, each class containing the communication methods that are available in a particular state of the protocol. Dardha et al., in Chapter 14, also start with a Scribble specification. Their StMungo tool generates an API as a single class with an associated typestate specification to constrain sequences of method calls. Code that uses the API can be checked for correctness with the Mungo typechecker. Finally, there are two chapters about programming with the MPI libraries. Chapter 15, by Ng and Yoshida, uses an extension of Scribble, called Pabble, to describe protocols that parametric in the number of runtime roles. From a Pabble specification they generate C code that uses MPI for communication and is guaranteed correct by construction. Chapter 16, by Ng et al., describes the ParTypes framework for analysing existing C+MPI programs with respect to protocols defined in an extension of Scribble. We hope that the book will serve a useful purpose as a report on the activities of COST Action IC1201 and as a survey of programming languages and tools based on behavioural types

Behavioural Types: from Theory to Tools

This book presents research produced by members of COST Action IC1201: Behavioural Types for Reliable Large-Scale Software Systems (BETTY), a European research network that was funded from October 2012 to October 2016. The technical theme of BETTY was the use of behavioural type systems in programming languages, to specify and verify properties of programs beyond the traditional use of type systems to describe data processing. A significant area within behavioural types is session types, which concerns the use of type-theoretic techniques to describe communication protocols so that static typechecking or dynamic monitoring can verify that protocols are implemented correctly. This is closely related to the topic of choreography, in which system design starts from a description of the overall communication flows. Another area is behavioural contracts, which describe the obligations of interacting agents in a way that enables blame to be attributed to the agent responsible for failed interaction. Type-theoretic techniques can also be used to analyse potential deadlocks due to cyclic dependencies between inter-process interactions. BETTY was organised into four Working Groups: (1) Foundations; (2) Security; (3) Programming Languages; (4) Tools and Applications. Working Groups 1–3 produced “state-of-the-art reports”, which originally intended to take snapshots of the field at the time the network started, but grew into substantial survey articles including much research carried out during the network [1–3]. The situation for Working Group 4 was different. When the network started, the community had produced relatively few implementations of programming languages or tools. One of the aims of the network was to encourage more implementation work, and this was a great success. The community as a whole has developed a greater interest in putting theoretical ideas into practice. The sixteen chapters in this book describe systems that were either completely developed, or substantially extended, during BETTY. The total of 41 co-authors represents a significant proportion of the active participants in the network (around 120 people who attended at least one meeting). The book is a report on the new state of the art created by BETTY in xv xvi Preface the area of Working Group 4, and the title “Behavioural Types: from Theory to Tools” summarises the trajectory of the community during the last four years. The book begins with two tutorials by Atzei et al. on contract-oriented design of distributed systems. Chapter 1 introduces the CO2 contract specifi- cation language and the Diogenes toolchain. Chapter 2 describes how timing constraints can be incorporated into the framework and checked with the CO2 middleware. Part of the CO2 middleware is a monitoring system, and the theme of monitoring continues in the next two chapters. In Chapter 3, Attard et al. present detectEr, a runtime monitoring tool for Erlang programs that allows correctness properties to be expressed in Hennessy-Milner logic. In Chapter 4, which is the first chapter about session types, Neykova and Yoshida describe a runtime verification framework for Python programs. Communication protocols are specified in the Scribble language, which is based on multiparty session types. The next three chapters deal with choreographic programming. In Chap- ter 5, Debois and Hildebrandt present a toolset for working with dynamic condition response (DCR) graphs, which are a graphical formalism for choreography. Chapter 6, by Lange et al., continues the graphical theme with ChorGram, a tool for synthesising global graphical choreographies from collections of communicating finite-state automata. Giallorenzo et al., in Chapter 7, consider runtime adaptation. They describe AIOCJ, a choreographic programming language in which runtime adaptation is supported with a guarantee that it doesn’t introduce deadlocks or races. Deadlock analysis is important in other settings too, and there are two more chapters about it. In Chapter 8, Padovani describes the Hypha tool, which uses a type-based approach to check deadlock-freedom and lock-freedom of systems modelled in a form of pi-calculus. In Chapter 9, Garcia and Laneve present a tool for analysing deadlocks in Java programs; this tool, called JaDA, is based on a behavioural type system. The next three chapters report on projects that have added session types to functional programming languages in order to support typechecking of communication-based code. In Chapter 10, Orchard and Yoshida describe an implementation of session types in Haskell, and survey several approaches to typechecking the linearity conditions required for safe session implemen- tation. In Chapter 11, Melgratti and Padovani describe an implementation of session types in OCaml. Their system uses runtime linearity checking. In Chapter 12, Lindley and Morris describe an extension of the web programming language Links with session types; their work contrasts with the previous two chapters in being less constrained by an existing language design. Continuing the theme of session types in programming languages, the next two chapters describe two approaches based on Java. Hu’s work, presented in Chapter 13, starts with the Scribble description of a multiparty session type and generates an API in the form of a collection of Java classes, each class containing the communication methods that are available in a particular state of the protocol. Dardha et al., in Chapter 14, also start with a Scribble specification. Their StMungo tool generates an API as a single class with an associated typestate specification to constrain sequences of method calls. Code that uses the API can be checked for correctness with the Mungo typechecker. Finally, there are two chapters about programming with the MPI libraries. Chapter 15, by Ng and Yoshida, uses an extension of Scribble, called Pabble, to describe protocols that parametric in the number of runtime roles. From a Pabble specification they generate C code that uses MPI for communication and is guaranteed correct by construction. Chapter 16, by Ng et al., describes the ParTypes framework for analysing existing C+MPI programs with respect to protocols defined in an extension of Scribble. We hope that the book will serve a useful purpose as a report on the activities of COST Action IC1201 and as a survey of programming languages and tools based on behavioural types

Behavioural Types

Behavioural type systems in programming languages support the specification and verification of properties of programs beyond the traditional use of type systems to describe data processing. A major example of such a property is correctness of communication in concurrent and distributed systems, motivated by the importance of structured communication in modern software. Behavioural Types: from Theory to Tools presents programming languages and software tools produced by members of COST Action IC1201: Behavioural Types for Reliable Large-Scale Software Systems, a European research network that was funded from October 2012 to October 2016. As a survey of the most recent developments in the application of behavioural type systems, it is a valuable reference for researchers in the field, as well as an introduction to the area for graduate students and software developers

Behavioural Types

Behavioural type systems in programming languages support the specification and verification of properties of programs beyond the traditional use of type systems to describe data processing. A major example of such a property is correctness of communication in concurrent and distributed systems, motivated by the importance of structured communication in modern software. Behavioural Types: from Theory to Tools presents programming languages and software tools produced by members of COST Action IC1201: Behavioural Types for Reliable Large-Scale Software Systems, a European research network that was funded from October 2012 to October 2016. As a survey of the most recent developments in the application of behavioural type systems, it is a valuable reference for researchers in the field, as well as an introduction to the area for graduate students and software developers

Cell libraries and verification

Digital electronic devices are often implemented using cell libraries to provide the basic logic elements, such as Boolean functions and on-chip memories. To be usable both during the development of chips, which is usually done in a hardware definition language, and for the final layout, which consists of lithographic masks, cells are described in multiple ways. Among these, there are multiple descriptions of the behavior of cells, for example one at the level of hardware definition languages, and another one in terms of transistors that are ultimately produced. Thus, correct functioning of the device depends also on the correctness of the cell library, requiring all views of a cell to correspond with each other. In this thesis, techniques are presented to verify some of these correspondences in cell libraries. First, a technique is presented to check that the functional description in a hardware definition language and the transistor netlist description implement the same behavior. For this purpose, a semantics is defined for the commonly used subset of the hardware definition language Verilog. This semantics is encoded into Boolean equations, which can also be extracted from a transistor netlist. A model checker is then used to prove equivalence of these two descriptions, or to provide a counterexample showing that they are different. Also in basic elements such as cells, there exists non-determinism reflecting internal behavior that cannot be controlled from the outside. It is however desired that such internal behavior does not lead to different externally observable behavior, i.e., to different computation results. This thesis presents a technique to efficiently check, both for hardware definition language descriptions and transistor netlist descriptions, whether non-determinism does have an effect on the observable computation or not. Power consumption of chips has become a very important topic, especially since devices become mobile and therefore are battery powered. Thus, in order to predict and to maximize battery life, the power consumption of cells should be measured and reduced in an efficient way. To achieve these goals, this thesis also takes the power consumption into account when analyzing non-deterministic behavior. Then, on the one hand, behaviors consuming the same amount of power have to be measured only once. On the other hand, functionally equivalent computations can be forced to consume the least amount of power without affecting the externally observable behavior of the cell, for example by introducing appropriate delays. A way to prevent externally observable non-deterministic behavior in practical hardware designs is by adding timing checks. These checks rule out certain input patterns which must not be generated by the environment of a cell. If an input pattern can be found that is not forbidden by any of the timing checks, yet allows non-deterministic behavior, then the cell’s environment is not sufficiently restricted and hence this usually indicates a forgotten timing check. Therefore, the check for non-determinism is extended to also respect these timing checks and to consider only counterexamples that are not ruled out. If such a counterexample can be found, then it gives an indication what timing checks need to be added. Because current hardware designs run at very high speeds, timing analysis of cells has become a very important issue. For this purpose, cell libraries include a description of the delay arcs present in a cell, giving an amount of time it takes for an input change to have propagated to the outputs of a cell. Also for these descriptions, it is desired that they reflect the actual behavior in the cell. On the one hand, a delay arc that never manifests itself may result in a clock frequency that is lower than necessary. On the other hand, a forgotten delay arc can cause the clock frequency being too high, impairing functioning of the final chip. To relate the functional description of a cell with its timing specification, this thesis presents techniques to check whether delay arcs are consistent with the functionality, and which list all possible delay arcs. Computing new output values of a cell given some new input values requires all connections among the transistors in a cell to obtain stable values. Hitherto it was assumed that such a stable situation will always be reached eventually. To actually check this, a wire is abstracted into a sequence of stable values. Using this abstraction, checking whether stable situations are always reached is reduced to analyzing that an infinite sequence of such stable values exists. This is known in the term rewriting literature as productivity, the infinitary equivalent to termination. The final contribution in this thesis are techniques to automatically prove productivity. For this purpose, existing termination proving tools for term rewriting are re-used to benefit from their tremendous strength and their continuous improvements