Introduction to "Mathematical Foundations for Software Engineering"

... He went on to prove that there was no solution to the Entscheidungsproblem by first showing that the halting problem for Turing machines is undecidable: it is not possible to decide, in general, algorithmically whether a given Turing machine will ever halt. (This proof depended on the notion of a Un ...

... He went on to prove that there was no solution to the Entscheidungsproblem by first showing that the halting problem for Turing machines is undecidable: it is not possible to decide, in general, algorithmically whether a given Turing machine will ever halt. (This proof depended on the notion of a Un ...

On Pebble Automata for Data Languages with

... cannot be determinized, see [1]. It was also shown that the satisfiability problem for the three-variable first order logic is undecidable. Another logical approach is via the so called linear temporal logic with n register freeze quantifier over the labels Σ, denoted LTL↓n (Σ, X, U), see [4]. It wa ...

... cannot be determinized, see [1]. It was also shown that the satisfiability problem for the three-variable first order logic is undecidable. Another logical approach is via the so called linear temporal logic with n register freeze quantifier over the labels Σ, denoted LTL↓n (Σ, X, U), see [4]. It wa ...

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... In the context of untimed systems, in the pioneering work [3, 4], the authors propose methods for synthesizing the synchronization skeleton of programs from their temporal logic specification. More recently, in [5–7], the authors investigate algorithmic methods to locally redesign fault-tolerant pro ...

... In the context of untimed systems, in the pioneering work [3, 4], the authors propose methods for synthesizing the synchronization skeleton of programs from their temporal logic specification. More recently, in [5–7], the authors investigate algorithmic methods to locally redesign fault-tolerant pro ...

pdf

... In [16, 17], the authors address the problem of synthesizing timed controllers with limited resources. Similar to the aforementioned work, the plant is modeled by a deterministic timed automaton, but the specification is given by an external nondeterministic timed automaton that describes undesired ...

... In [16, 17], the authors address the problem of synthesizing timed controllers with limited resources. Similar to the aforementioned work, the plant is modeled by a deterministic timed automaton, but the specification is given by an external nondeterministic timed automaton that describes undesired ...

Weighted Automata

... Under suitable assumptions (e.g., for computable fields) this problem is decidable [Sch61; BR11], as we shall see for probabilistic automata in Chapter 3. The emptiness problem can be refined when the semiring comes with an ordering, which, given a formal power series, allows us to classify words ac ...

... Under suitable assumptions (e.g., for computable fields) this problem is decidable [Sch61; BR11], as we shall see for probabilistic automata in Chapter 3. The emptiness problem can be refined when the semiring comes with an ordering, which, given a formal power series, allows us to classify words ac ...

GSC - ETSI docbox

... levels of EMF are not seen due to the considerable absorption by the humans inside these areas. Pacemaker malfunction due to cellular radio EMF will not occur at all in a train carriage even if several cellular radios are transmitting RF power at the maximum level simultaneously except for the vicin ...

... levels of EMF are not seen due to the considerable absorption by the humans inside these areas. Pacemaker malfunction due to cellular radio EMF will not occur at all in a train carriage even if several cellular radios are transmitting RF power at the maximum level simultaneously except for the vicin ...

Wolfram, Ch 12

... increase the computational power • Rule 110 is also universal … • CAs can emulate mobile automata, Turing Machines, substitution systems, register machines, number systems, logic circuits, RAMs, … – therefore CAs can emulate a general purpose computer, with simple rules and complex initial condition ...

... increase the computational power • Rule 110 is also universal … • CAs can emulate mobile automata, Turing Machines, substitution systems, register machines, number systems, logic circuits, RAMs, … – therefore CAs can emulate a general purpose computer, with simple rules and complex initial condition ...

Odd-Rule Cellular Automata on the Square Grid

... as 2512 , we describe the neighborhood F by a three-digit octal number, the “Odd-rule” number, obtained by reading the ON cells in the 3 × 3 grid from left to right, top to bottom. The canonical Odd-rule number for F is then the smallest of the Odd-rule numbers associated with any neighborhood that ...

... as 2512 , we describe the neighborhood F by a three-digit octal number, the “Odd-rule” number, obtained by reading the ON cells in the 3 × 3 grid from left to right, top to bottom. The canonical Odd-rule number for F is then the smallest of the Odd-rule numbers associated with any neighborhood that ...

1. Automata - CIS @ Temple University

... In mathematics and computer science, a “problem” is often defined as a function from input to output In principle, a function problem can be converted into a decision problem that only has “yes/no” answers So to solve a problem means to decide whether a given string belongs to a particular language ...

... In mathematics and computer science, a “problem” is often defined as a function from input to output In principle, a function problem can be converted into a decision problem that only has “yes/no” answers So to solve a problem means to decide whether a given string belongs to a particular language ...

Modelling Homeostatic Responses

... European Conference on Mathematical and Theoretical Biology 2011 Patricia Mostardinha University of Aveiro e-mail: [email protected] Fernão Vistulo de Abreu University of Aveiro ...

... European Conference on Mathematical and Theoretical Biology 2011 Patricia Mostardinha University of Aveiro e-mail: [email protected] Fernão Vistulo de Abreu University of Aveiro ...

# Cellular automaton

A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model studied in computability theory, mathematics, physics, complexity science, theoretical biology and microstructure modeling. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessellation structures, and iterative arrays.A cellular automaton consists of a regular grid of cells, each in one of a finite number of states, such as on and off (in contrast to a coupled map lattice). The grid can be in any finite number of dimensions. For each cell, a set of cells called its neighborhood is defined relative to the specified cell. An initial state (time t = 0) is selected by assigning a state for each cell. A new generation is created (advancing t by 1), according to some fixed rule (generally, a mathematical function) that determines the new state of each cell in terms of the current state of the cell and the states of the cells in its neighborhood. Typically, the rule for updating the state of cells is the same for each cell and does not change over time, and is applied to the whole grid simultaneously, though exceptions are known, such as the stochastic cellular automaton and asynchronous cellular automaton.The concept was originally discovered in the 1940s by Stanislaw Ulam and John von Neumann while they were contemporaries at Los Alamos National Laboratory. While studied by some throughout the 1950s and 1960s, it was not until the 1970s and Conway's Game of Life, a two-dimensional cellular automaton, that interest in the subject expanded beyond academia. In the 1980s, Stephen Wolfram engaged in a systematic study of one-dimensional cellular automata, or what he calls elementary cellular automata; his research assistant Matthew Cook showed that one of these rules is Turing-complete. Wolfram published A New Kind of Science in 2002, claiming that cellular automata have applications in many fields of science. These include computer processors and cryptography.The primary classifications of cellular automata, as outlined by Wolfram, are numbered one to four. They are, in order, automata in which patterns generally stabilize into homogeneity, automata in which patterns evolve into mostly stable or oscillating structures, automata in which patterns evolve in a seemingly chaotic fashion, and automata in which patterns become extremely complex and may last for a long time, with stable local structures. This last class are thought to be computationally universal, or capable of simulating a Turing machine. Special types of cellular automata are reversible, where only a single configuration leads directly to a subsequent one, and totalistic, in which the future value of individual cells depend on the total value of a group of neighboring cells. Cellular automata can simulate a variety of real-world systems, including biological and chemical ones.