A context-free language is a type of formal language that can be generated by a context-free grammar. It is a language that can be described by a set of production rules, where each rule consists of a non-terminal symbol (representing a category of phrases) and a sequence of terminal and/or non-terminal symbols.


Recognizing a language means determining whether a given input string belongs to the language or not. In the case of context-free languages, the recognition can be done by certain types of automata.


A finite state automaton, also known as a finite state machine, is a computational model that can be represented by a directed graph of states, where each state is connected by transitions labeled with input symbols. FSAs are commonly used to recognize regular languages, which are a subset of context-free languages. However, not all context-free languages can be recognized by an FSA.


A pushdown automaton is an extension of a finite state automaton that includes a stack. The stack allows the PDA to store and retrieve symbols during its computation. PDAs are more powerful than FSAs and can recognize context-free languages. The stack in a PDA allows it to keep track of the non-terminal symbols in the production rules and perform push and pop operations accordingly.


A linear bounded automaton is a more powerful computational model than PDAs. LBAs have a tape, similar to a Turing machine, which allows them to read, write, and move along an input string. LBAs are capable of recognizing context-sensitive languages, which are a superset of context-free languages.


Both PDAs and LBAs can recognize context-free languages. PDAs are specifically designed for recognizing context-free languages, while LBAs have the additional capability of recognizing context-sensitive languages. Therefore, the correct answer to the question is option 'D' - both (b) and (c) can recognize context-free languages.