The document discusses two algorithms for solving the critical section problem for multiple processes: 1. Peterson's algorithm from 1981 solves the problem for two processes using shared variables like flags and a turn variable to ensure only one process enters the critical section at a time. 2. Hofri's algorithm from 1990 generalizes the solution to N processes using an array of level variables and a turn array to designate the next process that can enter. Each process must pass through N "waiting rooms" represented by the increasing level values before entering the critical section.

1. Más sobre el algoritmo de Peterson Sistemas Operativos 2.0 UNITEC, Campus Tegucigalpa Egdares Futch H. Basado en Windows Operating System Internals - by David A. Solomon and Mark E. Russinovich with Andreas Polze

2. Solución para 2 procesos (Peterson - 1981) Shared variables of algorithms 1 and 2 - initialization: int flag[2]; flag[0] = flag[1] = 0; int turn = 0; Thread T i do { flag[i] = 1; turn = j; while ((flag[j] == 1) && turn == j) ; critical section flag[i] = 0; remainder section } while (1); Solves the critical-section problem for two threads.

3. Solución para N procesos (Hofri - 1990) N procesos, T 1 a T N-1 , N niveles/salas de espera: int level[n]; int turn[n-1]; // primer proceso=1 Thread T i do { for (k = 1 ; k < n ; k++) { level[i] = k; turn[k] = i; foreach (t != i) if (level[t] >= k && turn[k] == i) ; } level[i] = n; critical section level[i] = 0; remainder section } while (1);