Ahmed Saoudi

Weak alternating automata give a simple explanation of why most temporal and dynamic logics are decidable in exponential time

The authors give a very simple uniform explanation of the persistence of exponential decidability. They follow M. Vardi and P. Wolpers theory (1986) that given a formula gamma of a temporal or dynamic logic, it is important to construct an equivalent automation M/sub gamma /. They characterize the weak monadic theory of the tree; it turns out that weak alternating automata greatly simplify design procedures.<<ETX>>

Alternating automata, the weak monadic theory of trees and its complexity

Beginning with the fundamental article of Chandra et al. [2], the notation of alternation has clarified several results concerning the complexity of logical theories. Muller and Schupp [9] extended the idea of alternation to automata working on trees. Although such automata are a generalization of Rabin’s model [12] of nondeterministic automata working on infinite trees, complementation and, thus, all Boolean operations, are easy for such automata. In particular, complementation costs no extra states. There is, of course, no free lunch and, in the alternating model, one must pay for projection. Thus, alternating automata do not give a simple proof of Rabin’s fundamental theorem [12] on the decidability of the full monadic theory of the tree. Indeed, one must appeal to the powerful “forgetful determinacy” theorem of Gurevitch and Harrington [3] to show that alternating automata can be simulated by nondeterministic Rabin automata.

Parallel Image Analysis

In this lab you will be learning how to work with UPPMAX. You will enqueue image analysis jobs and collect their results. More often than not, you will write image analysis routines in MATLAB. However, running 20 MATLAB jobs at the same time would require 20 MATLAB licences. The way around this is to use the MATLAB compiler. Below I’ll explain how to compile your MATLAB script to a stand-alone executable, how to install that executable, and how to run it. We’ll use as an example the script and data you can get here: http://www.cb.uu.se/~cris/ParallelImageAnalysis/lab1.zip The ZIP file contains a script msrall.m that repeatedly calls measurethickness.m, using each of the names of the image files in the subdirectory. On a normal computer you’d call this script from within MATLAB, and the images would be processed sequentially. In this example, each image takes a minute or two to be processed. We will enqueue each of these independent tasks as a job on the UPPMAX cluster Kalkyl. They will then, depending on available nodes, be processed in parallel. Note that the measurement function does not return the results as an output variable, like you would normally do. Instead, the result of the computation is saved in a MAT file. The msrall.m script reads in all the MAT files and averages the results.

A quadtree algorithm for template matching on a pyramid computer

Abstract We present an algorithm to perform template matching of an N × N image with an M × M template on a (log N + 1)-levels pyramid computer. The time complexity of the algorithm is upper bounded by α log N + β M 2 , where α and β are constants.

EFFICIENT PARALLEL SHUFFLE RECOGNITION

This paper presents a parallel algorithm for verifying that a string X is formed by the shuffle of two strings Y and Z. The algorithm runs in O(log2n) time with O(n2/log2 n) processors on the EREW-PRAM model.

Context-Sensitivity of Puzzle Grammars

We study some properties of axray grammars, called puzzle grammars, introduced in [NS89].We give a new method, using puzzle grammar, for generating the set of rectangles. We prove the the emptiness problem for puzzle grammar is undecidable. We show that the non-overlapping problem for puzzle grammar is decidable.

Optimal Parallel Algorithms for Multidimensional Image Template Matching and Pattern Matching

This paper presents efficient and optimal parallel algorithms for multidimensional image template matching on CREW PRAM model. For an N d image and M d window, we present an optimal (resp. efficient) algorithm which runs in O(log(M)) time with O((M d ×N d )/log(M)) processors (resp.O(M d ×N d )). We also present efficient and optimal algorithms for solving the multidimensional array and pattern matching.

Pushdown Automata on Infinite Trees and Omega-Kleene closure of Context-Free Tree Sets

This theory has been extended to infinite trees ([II], [16], [17], [19], [22], [23], [25], [26], [27], [34]). In [23], M. O. Rabin proves that a set of infinite trees is weakly definable in

Automata on infinite objects and their applications to logic and programming

2S iff the set and its complement are recognizable by Bl~chi tree automata. D. E. Muller et al. [16] introduce weak alternating tree automata and characterize the weak monadic second order theory of the tree. In [20], M. Nivat and A. Saoudi characterize rational logic programs and prove that the equivalence of two rational logic programs is decidable, where two programs are equivalent if they compute the same set of tree~(i.e, copmutations). In another example M. Y. Vardi and P. Wolper [33] construct decision procedure for temporal logic of fair concurrent programs using automata on infinite trees.

Parallel recognition of high dimensional images

Abstract We introduce various types of ω-automata, top-down automata and bottom-up automata on infinite trees. We study the power of determinstic and nondeterministic tree automata and prove that deterministic and non-deterministic bottom-up tree automata accept the same infinite tree sets. We establish a relationship between tree automata, Logic programs, recursive program schemes, and the monadic second-order theory of the tree. We prove that the equivalence of two rational logic programs is decidable.