Cheat sheets

TOC-12Cheat sheet1 pageIn a paid pack

Push-Down Automata

The push-down automaton as a 7-tuple, the move label convention, instantaneous descriptions and the turnstile, acceptance by final state and by empty stack and their equivalence for nondeterministic PDAs, and constructions for a^n b^n, a^n b^2n, ww^R (nondeterministic, with a diagram), wcw^R, equal numbers of a and b, balanced parentheses and a^i b^j c^k with i = j or j = k. Every PDA was simulated nondeterministically on all strings up to length 7 or 8 and compared with its language.

Diagrams from TOC-12

TOC-13Cheat sheet1 pageIn a paid pack

DPDA, DCFL and CFG-PDA Equivalence

Deterministic PDAs and the deterministic context-free languages: the determinism condition, acceptance by final state versus empty stack and the prefix property, the proper inclusions regular in DCFL in CFL with witnesses, closure and decision facts that separate DCFLs from CFLs, unambiguity of DCFLs, the CFG to PDA construction (one state, expand on the stack) and the PDA to CFG triple construction with its variable count, and the solved 2025 question on what a DPDA accepts. The constructions were simulated on all strings up to length 8.