In this chapter, we present a hierarchy of infinite-state systems based on the primitive operations of sequential and parallel composition; the hierarchy includes a variety of commonly-studied classes of systems such as context-free and pushdown automata, and Petri net processes. We then examine the equivalence and regularity checking problems for these classes, with special emphasis on bisimulation equivalence, stressing the structural techniques which have been devised for solving these problems. Finally, we explore the model checking problem over these classes with respect to various linear- and branching-time temporal logics.

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Abstract. We introduce two abstract models for multithreaded programs based on dynamic networks of pushdown systems. We address the problem of symbolic reachability analysis for these models. More precisely, we consider the problem of computing effective representations of their reachability sets using finite-state automata. We show that, while forward reachability sets are not regular in general, backward reachability sets starting from regular sets of configurations are always regular. We provide algorithms for computing backward reachability sets using word/tree automata, and show how these algorithms can be applied for flow analysis of multithreaded programs. 1

ETAPS conference and he was taking part in a meeting. The next day I was giving a talk with the title “Grammars as Processes”, and Grzegorz, who had seen it announced in the program, asked me about it. We had little time, and so I could barely sketch the contents. I think Grzegorz would have liked the talk, because it pointed out an interesting connection between two of his oldest loves, formal languages and concurrency theory, and showed how a model of computation derived from this connection has a natural application in the area of program analysis. He would have also liked to see how an abstract result obtained by Büchi in 1964 on regular canonical systems was the basis to new algorithms for the analysis of software. This paper is a written version of the talk, and it also surveys the new results

Despite of the well-known state-explosion problem, certain simple but important data-flow analysis problems known as gen/kill problems can be solved e#ciently and completely for parallel programs with a shared state [7, 6, 2, 3, 13]. This paper shows that, in all probability, these surprising results cannot be generalized to significantly larger classes of data-flow analysis problems.

We present a fixpoint-based algorithm for context-sensitive interprocedural kill/gen-analysis of programs with thread creation. Our algorithm is precise up to abstraction of synchronization common in this line of research; it can handle forward as well as backward problems. We exploit a structural property of kill/gen-problems that allows us to analyze the influence of environment actions independently from the local transfer of data flow information. While this idea has been used for programs with parbegin/parend blocks before in work of Knoop/Steffen/Vollmer and Seidl/Steffen, considerable refinement and modification is needed to extend it to thread creation, in particular for backward problems. Our algorithm computes annotations for all program points in time depending linearly on the program size, thus being faster than a recently proposed automata based algorithm by Bouajjani et. al..

ABSTRACT. Multiset pushdown systems have been introduced by Sen and Viswanathan as an adequate model for asynchronous programs where some procedure calls can be stored as tasks to be processed later. The model is a pushdown system supplied with a multiset of pending tasks. Tasks may be added to the multiset at each transition, whereas a task is taken from the multiset only when the stack is empty. In this paper, we consider an extension of these models where tasks may be of different priority level, and can be preempted at any point of their execution by tasks of higher priority. We investigate the control point reachability problem for these models. Our main result is that this problem is decidable by reduction to the reachability problem for a decidable class of Petri nets with inhibitor arcs. We also identify two subclasses of these models for which the control point reachability problem is reducible respectively to the reachability problem and to the coverability problem for Petri nets (without inhibitor arcs). 1

We study conflict detection for programs with procedures, dynamic thread creation and a fixed finite set of (reentrant) monitors. We show that deciding the existence of a conflict is NP-complete for our model (that abstracts guarded branching by nondeterministic choice) and present a fixpoint-based complete conflict detection algorithm. Our algorithm needs worst-case exponential time in the number of monitors, but is linear in the program size.

Abstract. This paper presents an efficient, fixed point based algorithm for precise kill/gen analysis of interprocedural flow graphs with thread creation. The main idea of the algorithm is to separate a path reaching a control node into those steps required to reach the node and interfering steps, that are executed concurrently. These two parts are analyzed separately and combined afterwards. Exploiting the structure of kill/gen analysis we can show soundness and precision.

We propose a program analysis method for proving termination of recursive programs. The analysis is based on a reduction of termination to two separate problems: reachability of recursive programs, and termination of non-recursive programs. Our reduction works through a program transformation that modifies the call sites and removes return edges. In the new, non-recursive program, a procedure call may nondeterministically enter the procedure body (which means that it will never return) or apply a summary statement.