// ************************************************************************** // // // // eses eses // // eses eses // // eses eseses esesese eses Embedded Systems Group // // ese ese ese ese ese // // ese eseseses eseseses ese Department of Computer Science // // eses eses ese eses // // eses eseses eseseses eses University of Kaiserslautern // // eses eses // // // // ************************************************************************** // // Find the first element of an array that has a certain property. In the case// // below, the property has already been applied to form a boolean array, and // // thus, we seek the index of the first "true" in the array. // // The algorithm requires time O(1) using O(N^2) processors. // // ************************************************************************** // macro N = 16; module FirstOne([N]bool ?a,nat{N} index, event !rdy) { [N]bool x; // use O(N) processors to copy a to x; one might apply a desired property // to a[i] before copying, so that arbitrary properties can be checked for(i=0..N-1) x[i] = a[i]; // use O(N^2) processors to erase all x[i] that do not have the least index for(i=0..N-2) for(j=i+1..N-1) if(x[i] & x[j]) next(x[j]) = false; pause; // here, at most one x[i] is true; if so, i is the desired index for(i=0..N-1) if(x[i]) index = i; emit(rdy); } drivenby { for(i=0..N-1) a[i] = i==3 | i==5 | i==7; await(rdy); assert(a[index] -> forall(i=0..N-1) (i<index -> !a[i])); }