That we really can keep going indefinitely is justified by Hensel’s lemma, which will provide conditions under which the root of a polynomial mod p can be lifted to a root in Zp, such as the polynomial X 2 − 7 with p = 3: its two roots mod 3 can both be lifted to square roots of 7 in Z3. We will first give a basic version of Hensel’s lemma, illustrate it with examples, and then give a stronger ...

The pumping lemma for context-free languages is a result about pushdown automata which is strikingly similar to the well-known pumping lemma for regular languages. However, though the lemma for regular languages is simply proved by using the pigeonhole principle on deterministic automata, the lemma for pushdown automata is proven through an equivalence with context-free languages and through th...