K. Narayan Kumar

A theory of regular MSC languages

Message sequence charts (MSCs) are an attractive visual formalism widely used to capture system requirements during the early design stages in domains such as telecommunication software. It is fruitful to have mechanisms for specifying and reasoning about collections of MSCs so that errors can be detected even at the requirements level. We propose, accordingly, a notion of regularity for collections of MSCs and explore its basic properties. In particular, we provide an automata-theoretic characterization of regular MSC languages in terms of finite-state distributed automata called bounded message-passing automata. These automata consist of a set of sequential processes that communicate with each other by sending and receiving messages over bounded FIFO channels. We also provide a logical characterization in terms of a natural monadic second-order logic interpreted over MSCs. A commonly used technique to generate a collection of MSCs is to use a hierarchical message sequence chart (HMSC). We show that the class of languages arising from the so-called bounded HMSCs constitute a proper subclass of the class of regular MSC languages. In fact, we characterize the bounded HMSC languages as the subclass of regular MSC languages that are finitely generated.

Synthesizing Distributed Finite-State Systems from MSCs

Message sequence charts (MSCs) are an appealing visual formalism often used to capture system requirements in the early stages of design. An important question concerning MSCs is the following: how does one convert requirements represented by MSCs into state-based specifications? A first step in this direction was the definition in [9] of regular collections of MSCs, together with a characterization of this class in terms of finite-state distributed devices called message-passing automata. These automata are, in general, nondeterministic. In this paper, we strengthen this connection and describe how to directly associate a deterministic message-passing automaton with each regular collection of MSCs. Since real life distributed protocols are deterministic, our result is a more comprehensive solution to the synthesis problem for MSCs. Our result can be viewed as an extension of Zielonkas theorem for Mazurkiewicz trace languages [6, 19] to the setting of finite-state message-passing systems.

Logic Programming and Model Checking

We report on the current status of the LMC project, which seeks to deploy the latest developments in logic-programming technology to advance the state of the art of system specification and verification. In particular, the XMC model checker for value-passing CCS and the modal mu-calculus is discussed, as well as the XSB tabled logic programming system, on which XMC is based. Additionally, several ongoing efforts aimed at extending the LMC approach beyond traditional finite-state model checking are considered, including compositional model checking, the use of explicit induction techniques to model check parameterized systems, and the model checking of real-time systems. Finally, after a brief conclusion, future research directions are identified.

Verification of Parameterized Systems Using Logic Program Transformations

We show how the problem of verifying parameterized systems can be reduced to the problem of determining the equivalence of goals in a logic program. We further show how goal equivalences can be established using induction-based proofs. Such proofs rely on a powerful new theory of logic program transformations (encompassing unfold, fold and goal replacement over multiple recursive clauses), can be highly automated, and are applicable to a variety of network topologies, including uni- and bi-directional chains, rings, and trees of processes. Unfold transformations in our system correspond to algorithmic model-checking steps, fold and goal replacement correspond to deductive steps, and all three types of transformations can be arbitrarily interleaved within a proof. Our framework thus provides a seamless integration of algorithmic and deductive verification at fine levels of granularity.

MSO decidability of multi-pushdown systems via split-width

Multi-threaded programs with recursion are naturally modeled as multi-pushdown systems. The behaviors are represented as multiply nested words (MNWs), which are words enriched with additional binary relations for each stack matching a push operation with the corresponding pop operation. Any MNW can be decomposed by two basic and natural operations: shuffle of two sequences of factors and merge of consecutive factors of a sequence. We say that the split-width of a MNW is k if it admits a decomposition where the number of factors in each sequence is at most k. The MSO theory of MNWs with split-width k is decidable. We introduce two very general classes of MNWs that strictly generalize known decidable classes and prove their MSO decidability via their split-width and obtain comparable or better bounds of tree-width of known classes.

Model checking languages of data words

We consider the model-checking problem for data multi-pushdown automata (DMPA). DMPA generate data words, i.e, strings enriched with values from an infinite domain. The latter can be used to represent an unbounded number of process identifiers so that DMPA are suitable to model concurrent programs with dynamic process creation. To specify properties of data words, we use monadic second-order (MSO) logic, which comes with a predicate to test two word positions for data equality. While satisfiability for MSO logic is undecidable (even for weaker fragments such as first-order logic), our main result states that one can decide if all words generated by a DMPA satisfy a given formula from the full MSO logic.

Linear-Time model-checking for multithreaded programs under scope-bounding

We address the model checking problem of omega-regular linear-time properties for shared memory concurrent programs modeled as multi-pushdown systems. We consider here boolean programs with a finite number of threads and recursive procedures. It is well-known that the model checking problem is undecidable for this class of programs. In this paper, we investigate the decidability and the complexity of this problem under the assumption of scope-boundedness defined recently by La Torre and Napoli in [24]. A computation is scope-bounded if each pair of call and return events of a procedure executed by some thread must be separated by a bounded number of context-switches of that thread. The concept of scope-bounding generalizes the one of context-bounding [31] since it allows an unbounded number of context switches. Moreover, while context-bounding is adequate for reasoning about safety properties, scope-bounding is more suitable for reasoning about liveness properties that must be checked over infinite computations. It has been shown in [24] that the reachability problem for multi-pushdown systems under scope-bounding is PSPACE-complete. We prove in this paper that model-checking linear-time properties under scope-bounding is also decidable and is EXPTIME-complete.

Netcharts: Bridging the Gap between HMSCs and Executable Specifications

We define a new notation called netcharts for describing sets of message sequence chart scenarios (MSCs). Netcharts correspond to a distributed version of High-level Message Sequence Charts (HMSCs). Netcharts improve on HMSCs in two respects.

BEYOND TAMAKI-SATO STYLE UNFOLD/FOLD TRANSFORMATIONS FOR NORMAL LOGIC PROGRAMS

Unfold/fold transformation systems for logic programs have been extensively investigated. Existing unfold/fold transformation systems for normal logic programs typically fold using a single, non-recursive clause i.e. the folding transformation is very restricted. In this paper we present a transformation system that permits folding in the presence of recursion, disjunction, as well as negation. We show that the transformations are correct with respect to various model theoretic semantics of normal logic programs including the well-founded model and stable model semantics.

A Parameterized Unfold/Fold Transformation Framework for Definite Logic Programs

Given a program P, an unfold/fold program transformation system derives a sequence of programs P = P 0, P 1, ..., P n , such that P i + 1 is derived from P i by application of either an unfolding or a folding step. Existing unfold/fold transformation systems for definite logic programs differ from one another mainly in the kind of folding transformations they permit at each step. Some allow folding using a single (possibly recursive) clause while others permit folding using multiple non-recursive clauses. However, none allow folding using multiple recursive clauses that are drawn from some previous program in the transformation sequence. In this paper we develop a parameterized framework for unfold/fold transformations by suitably abstracting and extending the proofs of existing transformation systems. Various existing unfold/fold transformation systems can be obtained by instantiating the parameters of the framework. This framework enables us to not only understand the relative strengths and limitations of these systems but also construct new transformation systems. Specifically we present a more general transformation system that permits folding using multiple recursive clauses that can be drawn from any previous program in the transformation sequence. This new transformation system is also obtained by instantiating our parameterized framework.