ω-automaton

About: ω-automaton is a research topic. Over the lifetime, 2299 publications have been published within this topic receiving 68468 citations. The topic is also known as: stream automaton & ω-automata.

Applications of symbolic finite automata

Abstract: Symbolic automata theory lifts classical automata theory to rich alphabet theories. It does so by replacing an explicit alphabet with an alphabet described implicitly by a Boolean algebra. How does this lifting affect the basic algorithms that lay the foundation for modern automata theory and what is the incentive for doing this? We investigate these questions here. In our approach we use state-of-the-art constraint solving techniques for automata analysis that are both expressive and efficient, even for very large and infinite alphabets. We show how symbolic finite automata enable applications ranging from modern regex analysis to advanced web security analysis, that were out of reach with prior methods.

The Garden-of-Eden theorem for finite configurations

Abstract: In [l] Moore showed that the existence of mutually erasable configurations in a two-dimensional tessellation space is sufficient for the existence of Garden-of-Eden configurations. In [2 ] Myhill showed that the existence of mutually indistinguishable configurations is both necessary and sufficient for the existence of Garden-of-Eden configurations. After redefining the basic concepts with some minor changes in terminology, and after restating the main results from [l] and [2], we shall establish the equivalence between the existence of mutually erasable configurations and the existence of mutually indistinguishable configurations. This implies that the converse of Moore's result is true as well. We then show that by limiting the universe to the set of all finite configurations of the tessellation array, both of the above conditions remain sufficient, but neither is then necessary. Finally, we establish a necessary and sufficient condition for the existence of Garden-of-Eden configurations when only finite configurations are considered. I. The tessellation structure and the Garden-of-Eden theorems. The tessellation array, which was first used by Von Neumann [3] in obtaining his results on machine self-reproduction, can be visualized as an infinite two-dimensional Euclidean space divided into square cells, in the fashion of a checkerboard, where each cell can hold any symbol from a finite set A. We use the set Z2 of ordered pairs of integers to name the cells in the tessellation array. An array configuration, i.e., a symbol placed in each cell, is formally a mapping c'.Z2—>A. The restriction of an array configuration c to a subset 5 of Z2 will be denoted by (c)sWe speak of this as the configuration of S in array configuration c. Each cell will behave like a deterministic and synchronous finite-state machine, and the symbol in cell (i, j) at time / will depend on the symbol in cell (i, j) at time t — 1 as well as the symbols in certain neighboring cells at time t — 1. In this paper, as in [l] and [2], we fix the neighbors of any cell to be those cells (including the cell itself) which have each of their coordinates differing by at most 1 from the coordinate of the given cell. Figure 1 shows the neighbors of cell (i, j). Received by the editors September 2, 1969 and, in revised form, November 3, 1969. A MS subject classifications. Primary 0288, 0280, 9440.

Computing simulations over tree automata: efficient techniques for reducing tree automata

Abstract: We address the problem of computing simulation relations over tree automata. In particular, we consider downward and upward simulations on tree automata, which are, loosely speaking, analogous to forward and backward relations over word automata. We provide simple and efficient algorithms for computing these relations based on a reduction to the problem of computing simulations on labelled transition systems. Furthermore, we show that downward and upward relations can be combined to get relations compatible with the tree language equivalence, which can subsequently be used for an efficient size reduction of nondeterministic tree automata. This is of a very high interest, for instance, for symbolic verification methods such as regular model checking, which use tree automata to represent infinite sets of reachable configurations. We provide experimental results showing the efficiency of our algorithms on examples of tree automata taken from regular model checking computations.