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System-Level Specification and Modeling Languages
Published in Luciano Lavagno, Igor L. Markov, Grant Martin, Louis K. Scheffer, Electronic Design Automation for IC System Design, Verification, and Testing, 2017
Stephen A. Edwards, Joseph T. Buck
Our systems compute—perform tasks built from Boolean decision making and arithmetic—so it is natural to express them using a particular model of computation. Familiar models of computation include networks of Boolean logic gates and imperative software programming languages (e.g., C, assembly, Java). However, other, more specialized models of computation are often better suited for describing particular kinds of systems, such as those focused on digital signal processing.
Topology and Logic Programming
Published in Pascal Hitzler, Anthony Seda, Mathematical Aspects of Logic Programming Semantics, 2016
In this chapter, we consider the role of topology in logic programming semantics. There is a considerable history of topology being used in computer science in general, much of it stemming from the role of the Scott topology in domain theory and in conventional programming language semantics. However, topological methods have been employed in a number of other areas of importance in computing, including digital topology in image processing, software engineering, and the use of metric spaces in concurrency, for example. In addition, topological methods and ideas have been used in foundational investigations via the topology of observable properties of M.B. Smyth, see [Smyth, 1992]. Again, Blair et al. have made considerable use of convergence spaces in unifying discrete and continuous models of computation and, hence, in providing models for hybrid systems. Indeed, these authors, see [Blair et al., 1999] and [Blair and Remmel, 2001], for example, view any model of computation in which there is a notion of evolving state as a dynamical system. Such models of computation include, of course, Turing machines, finite state machines, logic programs, neural networks, etc. On the other hand, convergence spaces, as already noted earlier, provide a very general framework in which to study convergence and continuity, either by means of nets or by filters, and include topologies as a special case. It is shown in [Blair et al., 1999] and [Blair and Remmel, 2001] that the execution traces of a dynamical system can be realized as those solutions of a certain type of constraint on a convergence space that yield continuous instances of the constraint. This work provides a foundation for hybrid systems. Furthermore, the papers [Blair et al., 1997a, Blair et al., 1997b, Blair, 2007, Blair et al., 2007] give many other interesting applications of ideas of a dynamical systems and analytical nature to the theory of computation, including logic programming in particular.
An approach integrating planning and image-based visual servo control for road following and moving obstacles avoidance
Published in International Journal of Control, 2020
Ramses Reyes, Rafael Murrieta-Cid
A finite-state machine (FSM) or automaton is defined as a mathematical model of computation, it is conceived as an abstract machine that can be in one of a finite number of states (Hopcroft, Motwani, & Ullman, 2000). Figure 2 shows a graphical representation of an automaton corresponding to the general plan or strategy to follow the road and pass or avoid collision with other cars. The automaton has five states: Start, Following left lane, Following right lane, Changing to left lane and Changing to right lane. The transitions among the states are represented with arrows, each arrow has a label corresponding to the observation (or condition) required to given a state change to other state. A state corresponds to the general internal condition of the robot, in each one of these states two variables are controlled: (1) the position in the image of the centre of the lane that the robot follows, which is regulated through the angular velocity of the vehicle and (2) the linear velocity of the vehicle, which depends on the presence or absence of obstacles and the curvature of the road. In our current implementation, the state Start is trivial, the automaton immediately transits to state Following right line, since we assume that the car starts on the right lane. It would be possible to extend this state to reach the road starting with the car placed outside the track.