How do we construct a context-free grammar (CFG) from a given PDA to recognize the same set of strings?
To construct a context-free grammar (CFG) from a given pushdown automaton (PDA) to recognize the same set of strings, we need to follow a systematic approach. This process involves converting the PDA's transition function into production rules for the CFG. By doing so, we establish an equivalence between the PDA and the CFG, ensuring that
Describe the process of designing a context-sensitive grammar for a language consisting of strings with an equal number of ones, twos, and threes.
Designing a context-sensitive grammar for a language consisting of strings with an equal number of ones, twos, and threes involves several steps and considerations. Context-sensitive grammars are a type of formal grammar that generate languages that can be recognized by linear-bounded automata. These grammars are more expressive than regular grammars and context-free grammars, as they
What is the Chomsky hierarchy of languages and how does it classify formal grammars based on their generative power?
The Chomsky hierarchy of languages is a classification system that categorizes formal grammars based on their generative power. It was proposed by Noam Chomsky, a renowned linguist and computer scientist, in the 1950s. The hierarchy consists of four levels, each representing a different class of formal languages. These levels are known as Type-3 (Regular), Type-2