Pick all true statements about formal languages:

Question

BlackTom AI · Accepted Answer

A finite language can always be described by a finite regular expression or accepted by a finite automaton, so "All finite languages are regular" is true.

Relevant concepts:
- Regular languages are those accepted by finite automata (DFA/NFA), or equivalently described by regular expressions or regular grammars.
- A finite language is a language containing a finite number of strings.
- Closure properties: regular languages are closed under finite union; each single string is regular.

Step-by-step reasoning and construction:
1. Let L = {w1, w2, ..., wk} be any finite language (k is finite). Each individual string wi is a regular language because a deterministic finite automaton (DFA) can be built that reads exactly wi and ends in an accepting state. Concretely, for wi of length n create n+1 states forming a path labeled by the symbols of wi; only the final state is accepting.
2. Regular languages are closed under finite union. Therefore the union of the k regular single-string languages {w1} ∪ {w2} ∪ ... ∪ {wk} is regular.
3. Equivalently, form the regular expression w1|w2|...|wk (or w1 + w2 + ... + wk). This regular expression denotes L, so L is regular.
4. So every finite language admits a regular expression and a finite automaton; hence all finite languages are regular.

Why the other options are incorrect:
- "All finite languages are non-regular." This contradicts the construction above; finite languages are regular, not non-regular.
- "All infinite languages are non-regular." False: many infinite languages are regular, e.g., a*, (a+b)*, or the set of all strings with an even number of a's. These are infinite and regular.
- "All infinite languages are regular." Also false: some infinite languages are not regular; for example L = {a^n b^n | n ≥ 0} is infinite but non-regular (can be shown by the pumping lemma).

Conclusion: The only correct statement is "All finite languages are regular," which matches the provided answer.

Pick all true statements about formal languages:Multiple choice

Similar Questions

A language L is regular if: (Pick all true statements)

Both the Deterministic and Non-Deterministic finite automata are equivalent in expressive power to the language of regular expressions.

Pick all non-regular languages: Notes Assume they are defined over the appropriate Sigma. Spaces are added to the patterns for readability purpose.

If L1 and L2 are regular languages, pick which of the following operations produce a regular language:

Which one is correct?

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler