Complexity of analysis and verification problems for communicating automata and discrete dynamical systems.

We identify several simple but powerful concepts, techniques, and results; and we use them to characterize the complexities of a number of basic problems II, that arise in the analysis and verification of the following models M of communicating automata and discrete dynamical systems: systems of communicating automata including both finite and infinite cellular automata, transition systems, discrete dynamical systems, and succinctly-specified finite automata. These concepts, techniques, and results are centered on the following: (1) reductions Of STATE-REACHABILITY problems, especially for very simple systems of communicating copies of a single simple finite automaton, (2) reductions of generalized CNF satisfiability problems [Sc78], especially to very simple communicating systems of copies of a few basic acyclic finite sequential machines, and (3) reductions of the EMPTINESS and EMPTINESS-OF-INTERSECTION problems, for several kinds of regular set descriptors. For systems of communicating automata and transition systems, the problems studied include: all equivalence relations and simulation preorders in the Linear-time/Branching-time hierarchies of equivalence relations and simulation preorders of [vG90, vG93], both without and with the hiding abstraction. For discrete dynamical systems, the problems studied include the INITIAL and BOUNDARY VALUE PROBLEMS (denoted IVPs and BVPs, respectively), for nonlinear difference equations over many different algebraic structures, e.g. all unitary rings, all finite unitary semirings, and all lattices. For succinctly specified finite automata, the problems studied also include the several problems studied in [AY98], e.g. the EMPTINESS, EMPTINESS-OF-INTERSECTION, EQUIVALENCE and CONTAINMENT problems. The concepts, techniques, and results presented unify and significantly extend many of the known results in the literature, e.g. [Wo86, Gu89, BPT91, GM92, Ra92, HT94, SH+96, AY98, AKY99, RH93, SM73, Hu73, HRS76, HR78], for communicating automata including both finite and infinite cellular automata and for finite automata specified by special kinds of context-free grammars, by regular operations augmented with squaring and intersection, and specified succinctly as in [AY98, AKY99]. Moreover, our development of these concepts, techniques, and results shows how several ideas, techniques, and results, for the individual models M above can be extended to apply to all or to most of these models. As one example of this and paraphrasing [BPTBl] , we show that most of these models M exhibit computationally-intractable sensitive dependence on initial conditions, for the same reason. These computationally-intractable sensitivities range from PSPACE-hard to undecidable

An SDS Modeling Approach for Simulation-Based Control

We initiate a study of mathematical models for specifying (discrete) simulation-based control systems. It is desirable to specify simulation-based control systems using a model that is intuitive, succinct, expressive, and whose state space properties are relatively easy computationally. We compare automata-based models for specifying control systems and find that all systems that are currently used (such as finite state machines, communicating hierarchical finite state machines (FSM), communicating finite state machines, and Turing machines) lack at least one of the abovementioned features. We propose using sequential dynamical systems (SDS) - a formalism for representing discrete simulations - to specify simulation-based control systems. We show how to adapt the standard SDS model to specify cell-level controllers for a generic cell. For reasonable flexible manufacturing cells, the SDS-based specification has size polynomial in the size of the cell, while in the worst case the FSM-based specification has size exponential in the size of the cell

An SDS Modeling Approach for Simulation-Based Control

We initiate a study of mathematical models for specifying (discrete) simulation-based control systems. It is desirable to specify simulation-based control systems using a model that is intuitive, succinct, expressive, and whose state space properties are relatively easy computationally. We compare automata-based models for specifying control systems and find that all systems that are currently used (such as finite state machines, communicating hierarchical finite state machines (FSM), communicating finite state machines, and Turing machines) lack at least one of the abovementioned features. We propose using sequential dynamical systems (SDS) - a formalism for representing discrete simulations - to specify simulation-based control systems. We show how to adapt the standard SDS model to specify cell-level controllers for a generic cell. For reasonable flexible manufacturing cells, the SDS-based specification has size polynomial in the size of the cell, while in the worst case the FSM-based specification has size exponential in the size of the cell

Dichotomy Results for Fixed Point Counting in Boolean Dynamical Systems

We present dichotomy theorems regarding the computational complexity of counting fixed points in boolean (discrete) dynamical systems, i.e., finite discrete dynamical systems over the domain {0,1}. For a class F of boolean functions and a class G of graphs, an (F,G)-system is a boolean dynamical system with local transitions functions lying in F and graphs in G. We show that, if local transition functions are given by lookup tables, then the following complexity classification holds: Let F be a class of boolean functions closed under superposition and let G be a graph class closed under taking minors. If F contains all min-functions, all max-functions, or all self-dual and monotone functions, and G contains all planar graphs, then it is #P-complete to compute the number of fixed points in an (F,G)-system; otherwise it is computable in polynomial time. We also prove a dichotomy theorem for the case that local transition functions are given by formulas (over logical bases). This theorem has a significantly more complicated structure than the theorem for lookup tables. A corresponding theorem for boolean circuits coincides with the theorem for formulas.Comment: 16 pages, extended abstract presented at 10th Italian Conference on Theoretical Computer Science (ICTCS'2007

Elements of a Theory of Simulation

Unlike computation or the numerical analysis of differential equations, simulation does not have a well established conceptual and mathematical foundation. Simulation is an arguable unique union of modeling and computation. However, simulation also qualifies as a separate species of system representation with its own motivations, characteristics, and implications. This work outlines how simulation can be rooted in mathematics and shows which properties some of the elements of such a mathematical framework has. The properties of simulation are described and analyzed in terms of properties of dynamical systems. It is shown how and why a simulation produces emergent behavior and why the analysis of the dynamics of the system being simulated always is an analysis of emergent phenomena. A notion of a universal simulator and the definition of simulatability is proposed. This allows a description of conditions under which simulations can distribute update functions over system components, thereby determining simulatability. The connection between the notion of simulatability and the notion of computability is defined and the concepts are distinguished. The basis of practical detection methods for determining effectively non-simulatable systems in practice is presented. The conceptual framework is illustrated through examples from molecular self-assembly end engineering.Comment: Also available via http://studguppy.tsasa.lanl.gov/research_team/ Keywords: simulatability, computability, dynamics, emergence, system representation, universal simulato

CSP channels for CAN-bus connected embedded control systems

Closed loop control system typically contains multitude of sensors and actuators operated simultaneously. So they are parallel and distributed in its essence. But when mapping this parallelism to software, lot of obstacles concerning multithreading communication and synchronization issues arise. To overcome this problem, the CT kernel/library based on CSP algebra has been developed. This project (TES.5410) is about developing communication extension to the CT library to make it applicable in distributed systems. Since the library is tailored for control systems, properties and requirements of control systems are taken into special consideration. Applicability of existing middleware solutions is examined. A comparison of applicable fieldbus protocols is done in order to determine most suitable ones and CAN fieldbus is chosen to be first fieldbus used. Brief overview of CSP and existing CSP based libraries is given. Middleware architecture is proposed along with few novel ideas

Modeling Time in Computing: A Taxonomy and a Comparative Survey

The increasing relevance of areas such as real-time and embedded systems, pervasive computing, hybrid systems control, and biological and social systems modeling is bringing a growing attention to the temporal aspects of computing, not only in the computer science domain, but also in more traditional fields of engineering. This article surveys various approaches to the formal modeling and analysis of the temporal features of computer-based systems, with a level of detail that is suitable also for non-specialists. In doing so, it provides a unifying framework, rather than just a comprehensive list of formalisms. The paper first lays out some key dimensions along which the various formalisms can be evaluated and compared. Then, a significant sample of formalisms for time modeling in computing are presented and discussed according to these dimensions. The adopted perspective is, to some extent, historical, going from "traditional" models and formalisms to more modern ones.Comment: More typos fixe