# Tagged Questions

Automata Theory, including abstract machines, grammars, parsing, grammatical inference, transducers, and finite-state techniques

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### Designing a deterministic finite automata

How would I go about designing a deterministic finite automata to recognize the language L = {λ, ab, abab, ababab, . . . } consisting of strings that start with ‘a’, end with ‘b’, and alternate in ...
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### Deterministic finite automata [closed]

For this question about Deterministic finite automata: Is this answer: bbbb, bbba, bbab, bbaa, b, a correct?
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### equivalence class for language in Theory of automata

we say x,y is equivalent to language L, if for any $z \in L$ we have: $xz \in L \Longleftrightarrow yz \in L$. for $L= (ab \cup aab)^*$, what is the equivalence class for L? my professor ...
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### Input and output of a Turing machine

For some machine models of computation there is no question what their input and output is: it's just the contents of some specific "cells", e.g. on a "tape" isomorphic to $\mathbb{N}$. Consider for ...
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### Use the power-set construction to find a deterministic automata

Given a nondeterministc automata N, how do you use the power-set construction to find a deterministic automata that recognizes L(N)? Here is my work so far: We can start in state 1, 2. If we get ...
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### Lattice worms with nontrivial deaths

In Paterson's worms, a triangular lattice is used. A worm can move in 6 directions. As each node is hit, the worm follows an internal rule for which edge it will eat next based on the edges already ...
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### Regular Language and Unknown Operation

I read the $L$ is a Regular language. Define $L'$ as following: $$L'=\{a_2a_1a_4a_3\ldots a_{2n}a_{2n-1}\mid a_1a_2\ldots a_{2n} \in L\}.$$ why $L'$ is Regular? any hint or idea would be highly ...
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### A CFG Grammar for One Language

Suppose : $w_1,w_2 \in \{a,b\}^∗$ and $L=\{w_1w_2 \mid w_1,w_2 \in \{a,b\}^* \land n_a(w_1)=n_b(w_2)\}$ $n_a$ is number of $a$'s and $n_b$ is number of $b$'s. This is a Entrance Exam question. I ...
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### Challenge on Property of Complement in Language

We have: and M be a finite automata. Suppose d(M) be a deterministic automata that equivalence to M. if $M_1$ and $M_2$ be two finite automata, $M_1 + M_2$ is the finite automata such that the ...
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### Algorithm that takes input desc. of two PDAs and outputs intersection of langs. recognized by two PDAs

Does there exist an algorithm which takes as input the descriptions of two pushdown automata, $P1$ and $P2$, and prints the description of another pushdown automaton which recognizes the intersection ...
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### Deciding TM which fails to halt whenever the length of its input string is a prime number

I have the following Statement: "A TM called $A$ which fails to halt (i.e runs forever) whenever the length of its input string is a prime number, and eventually halts for all other input strings" ...
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### disproving union of infinitely many regular languages

I want to disprove the following statement: "if $L$ is the union of infinitely many regular languages, then $L$ is guaranteed to be a regular language." I don't know where to start. Any hint will be ...
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### Complex automata Rubiks cube question (with picture) help needed

Question 1 A Rubik’s Cube is a puzzle in the shape of a cube. Each face is covered by nine stickers, each of which is coloured with one of six colours: white, red, blue, orange, green, andyellow. An ...
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### Design an finite automata for 010 and 01? [duplicate]

I have tried below question for designing automata but didn't success . ...
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### Checking my CFG to CNF answer

I attempted to transform the given CFG into CNF. $$S → ASA|A$$ $$A→aa|ε$$ Here are my steps: $$S→X$$ $$X→XA|AX|A$$ $$A→aa$$ $$S→X$$ $$X→XA|AX|YY$$ $$A→YY$$ $$Y→a$$ $$S→XA|AX|YY$$ X→XA|AX|...
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### Create a finite-state machine

I need to create a finite-state machine which accepts strings whose characters are in {a,b,c} and produce output strings of T's and F's. The machine outputs a T once the characters ab is encountered ...
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### minimal DFA with four states

I want to minimal this DFA: But i don't know what to do. Anyone can help me? Thanks
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### Proving context free language membership is $P$ complete with respect to log-space reductions

This is exercise from Introduction to Automata theory, Languages and Computation, by Hopcrof, Ullman (first edition). I found example of polynomial reduction to some problems in logic, or graph theory,...