. Hierarchical state machines are finite state machines whose states themselves can be other machines. In spite of their popularity in many modeling tools for software design, very little is known concerning their complexity and expressiveness. In this paper, we study these questions for hierarchical state machines as well as for communicating hierarchical state machines, that is, finite state machines extended with both hierarchy and concurrency. We present a comprehensive set of results characterizing (1) the complexity of the reachability, emptiness and universality problems, (2) the complexity of the language inclusion and equivalence problems, and (3) the succinctness relationships between different types of machines. 1 Introduction Finite state machines (FSMs) are widely used in the modeling of systems in various areas. Descriptions using FSMs are useful to represent the flow of control (as opposed to data manipulation) and are amenable to formal analysis such as model checking ...

We study an automata-theoretic approach to planning for temporally extended goals. Specifically, we devise techniques based on nonemptiness of Büchi automata on infinite words, to synthesize sequential and conditional plans in a generalized setting in which we have that: goals are general temporal properties of desired execution; dynamic systems are represented by finite transition systems; incomplete information on the initial situation is allowed; and states are only partially observable. We prove that the techniques proposed are optimal wrt the worst case complexity of the problem. Thanks to the scalability of the nonemptiness algorithms, the techniques presented here promise to be applicable to fairly large systems, notwithstanding the intrinsic complexity of the problem.

Several formalisms and tools for software development use hierarchy for system design, for instance statecharts and diagrams in UML. Message sequence charts are an ITU standardized notation for asynchronously communicating processes. The standard Z.120 allows (high-level) MSC-references that correspond to the use of macros. We consider in this paper two basic verification tasks for hierarchical MSCs (nested high-level MSCs, nHMSC), the membership and the pattern matching problem. We show that the membership problem for nHMSCs is PSPACE-complete, even using a weaker semantics for nMSCs than the partial-order semantics. For pattern matching nMSCs M;N we exhibit a polynomial algorithm of time O(jM j 2 \Delta jN j 2 ). We use here techniques stemming from algorithms on compressed texts.

Summary We describe an interaction based approach for computer modeling and simulation of large integrated biological, information, social and technical (BIST) systems 1 Examples of such systems are urban regional transportation systems, the national electrical power markets and grids, gene regulatory networks, the worldwide Internet, infectious diseases, vaccine design and deployment, theater war, etc. These systems are composed of large numbers of interacting human, physical, informational and technological components. These components adapt and learn, exhibit perception, interpretation, reasoning, deception, cooperation and non-cooperation, and have economic motives as well as the usual physical properties of interaction. The theoretical foundation of our approach consists of two parts: (i) mathematics of complex interdependent dynamic networks, and (ii) mathematical and computational theory of a class of finite discrete dynamical systems called Sequential Dynamical Systems (SDSs). We then consider engineering principles based on such a theory. As with the theoretical foundation, they consist of two basic parts: (i) Efficient data manipulation, including synthesis, integration, storage and regeneration and (ii) high performance computing oriented system design, development and implementation. The engineering methods allow us to specify, design, and analyze simulations of extremely large systems and implement them on massively parallel architectures. As an illustration of our approach, an interaction based computer modeling and simulation framework to study very large interdependent societal infrastructures is described. 1

Transaction Datalog (abbreviated T D) is a concurrent programming language that provides process modeling, database access, and advanced transactions. This paper illustrates the use of T D for specifying and simulating workflows, with examples based on the needs of a high-throughput genome laboratory. In addition to database support, these needs include concurrent access to shared resources, synchronization of work, and networks of cooperating workflows. We also use T D to explore the computational complexity of workflows in data-intensive applications. We show, for instance, that workflows can be vastly more complex than database transactions, largely because concurrent processes can interact and communicate via the database (i:e:, one process can read what another one writes). We then investigate the sources of this complexity, focusing on features for data modeling and process modeling. We show that by carefully controlling these features, the complexity of workflows can be reduced ...

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In order to check whether an open system satisfies a desired property, we need to check the behavior of the system with respect to an arbitrary environment. In the most general setting, the environment is another open system. Given an open system � and a property � , we say that � robustly satisfies � iff for every open system �� � , which serves as an environment to � , the composition ���� � � satisfies �. The problem of robust model checking is then to decide, given � and � , whether � robustly satisfies �. In this paper we study the robust-model-checking problem. We consider systems modeled by nondeterministic Moore machines, and properties specified by branching temporal logic (for linear temporal logic, robust satisfaction coincides with usual satisfaction). We show that the complexity of the problem is EXPTIME-complete for CTL and the �-calculus, and is 2EXPTIME-complete for CTL �. We partition branching temporal logic formulas into three classes: universal, existential, and mixed formulas. We show that each class has different sensitivity to the robustness requirement. In particular, unless the formula is mixed, robust model checking can ignore nondeterministic environments. In addition, we show that the problem of classifying a CTL formula into these classes is EXPTIME-complete.

this paper concurrent transition systems, where communication between concurrent components is modeled explicitly. Assuming boundedness of the treewidth of the communication graph, which we refer to as local treewidth, is reasonable, since the topology of communication in concurrent systems is often constrained physically

Computer simulation is a computational approach whereby global system properties are produced as dynamics by direct computation of interactions among representations of local system elements. A mathematical theory of simulation consists of an account of the formal properties of sequential evaluation and composition of interdependent local mappings. When certain local mappings and their interdependencies can be related to particular real world objects and interdependencies, it is common to compute the interactions to derive a symbolic model of the global system made up of the corresponding interdependent objects. The formal mathematical and computational account of the simulation provides a particular kind of theoretical explanation of the global system properties and, therefore, insight into how to engineer a complex system to exhibit those properties. This paper considers the mathematical foundations and engineering principles necessary for building large scale simulations of socio-technical systems. Examples of such systems are urban regional transportation systems, the national electrical power markets and grid, the world-wide Internet, vaccine design and deployment, theater war, etc. These systems are composed of large numbers of interacting human, physical and technological components. Some components adapt and learn, exhibit perception, interpretation, reasoning, deception, cooperation and non-cooperation, and economic motives as well as the usual physical properties of interaction. The systems themselves are large and the behavior of sociotechnical systems is tremendously complex.

Abstract. In the automata-theoretic approach to formal verification, the satisfiability and the model-checking problems for linear temporal logics are reduced to the nonemptiness problem of automata on infinite words. Modifying the nonemptiness algorithm to return a shortest witness to the nonemptiness (that is, a word of the form uv ω that is accepted by the automaton and for which |uv | is minimal) has applications in synthesis and counterexample analysis. Unlike shortest accepting runs, which have been studied in the literature, the definition of shortest witnesses is semantic and is independent on the specification formalism of the property or the system. In particular, its robustness makes it appropriate for analyzing counterexamples of concurrent systems. We study the problem of finding shortest witnesses in automata with various types of concurrency. We show that while finding shortest witnesses is more complex than just checking nonemptiness in the nondeterministic and in the concurrent models of computation, it is not more complex in the alternating model. It follows that when the system is the composition of concurrent components, finding a shortest counterexample to its correctness is not harder than finding some counterexample. Our results give a computational motivation to translating temporal logic formulas to alternating automata, rather than going all the way to nondeterministic automata. 1