1 transparent par page - Montefiore

hapter Exemples 5 Induction
start
state
0 1 2 99 overflow
Un compteur Figure : 5.6 State transitions for the 99-bounded counter.
◮ Q = {0, 1, . . . , 99, overflow}
◮ Q0 = {0}
achines
◮ δ = {n → n + 1|0 ≤ n < 99} {99 → overflow, overflow →
overflow}
tateLemachines taquin : are a simple abstract model of step-by-step processes. Since com
uter programs ◮ Q =l’ensemble can be understood des configurations as defining possibles step-by-step du taquin, computational |Q| = 16! processe
’s not◮surprising Q0 = {lathat configuration state machines initiale} come up regularly in computer science. Th
lso come ◮ δ = up{〈config1, in many other config2〉| settings config2 such peut as s’obtenir designingà digital partir de circuits config1 and enmo
ling probabilistic un mouvement} processes. This section introduces Floyd’s Invariant Princip
hich is a version of induction tailored specifically for proving properties of sta
78