0
votes
2answers
47 views

The language of TMs accepting some word starting with 101

I have a homework question about the properties (decidability, Turing-recognizability, etc.) of the language $$ L = \{ \langle M \rangle | \text{$M$ is a TM and $M$ accepts some string $w$ which has ...
5
votes
2answers
53 views

Intersection of two NPDAs

Is there a way to take the interection of two NPDAs? I can't seem to find anything that can make that happen, but it seems like the type of thing that is should be relatively trival.
1
vote
1answer
20 views

In reference to the Chomsky hierarchy (and automatas), Which is the linear feedback shift register Languages/automaton?

The Chomsky hierarchy is a guideline on language expressive power. The linear feedback shift register is a very interesting "element" to structure a language and there is a large theoretical ...
2
votes
3answers
86 views

Language Recognition Devices and Language Generators

I have few CS textbooks with me which discuss languages, well actually 2 plus old course notes supplied a few years ago. I have been searching the web too any only seem to come up with vague responses ...
2
votes
0answers
50 views

Prove Single-Tape and Non-write Turing Machine can Only Recognize Regular Language?

Here is the problem: Prove the single-tape TM that cannot write on the portion of the tape containing the input string recognize only regular language. My idea is to prove that this particular TM ...
1
vote
1answer
74 views

Can reversing the final and non-final states of a DFA produce the complement of the original language?

Is this true? If I change all final states of a given Deterministic Finite Automata to non final states and all non final states to final states then does this new automata represent the complement of ...
5
votes
1answer
73 views

How to find a Deterministic PDA for an intersection of languages

There are two languages, $\qquad L_1 = \{w\in\{a,b\}^*: N_a\leq N_b\}$ and $\qquad L_2=\{w\in\{a,b\}^*: N_b\leq 2N_a\}$ where $N_a$ means the number of occurrences of $a$ in the string $w$. Same ...
3
votes
1answer
70 views

NFA to DFA final states proof

When translating an NFA into an equivalent DFA, we can say that all states that contain the final states of NFA, is the final state of DFA. What should my arguments be in order to prove this? ...
3
votes
1answer
40 views

If L is a non-regular language over {a}, are all Myhill-Nerode classes singletons?

Is there a non-regular language over unary alphabet $\{a\}$ which has a Myhill-Nerode equivalence class that is not a singleton?
1
vote
1answer
40 views

Finite Automata Input Confusion

I am looking at the following non-deterministic finite automata which accepts all strings that end with at least 2 bs. I am wondering what would happen when you have the input string 'abba' with this ...
0
votes
2answers
80 views

Why does a regular expression only accept all my required strings when the concatenation is the first of the OR operations?

I am having a bit of difficulty understanding the order of precedence in boolean logic for the OR operation. Take this example: Assume the following regular expression: ...
6
votes
3answers
132 views

Demonstrate that DPDA is closed under complement by construction

I've been trying for quite some extended time to find a construction so that I can formally demonstrate that a deterministic PDA is closed under complementation. However, it happens that every idea I ...
3
votes
2answers
111 views

What does the symbol # mean when it comes to languages

Given the following: $$\{ w\#x \mid w^R \text{ is a substring of $x$, with $x$ and $w \in \Sigma^*$} \}$$ What does $w\#x$ denote?
0
votes
1answer
87 views

Turing machine with possible transitions to the final state [closed]

Let's say we want to draw the transition graph of a Turing Machine that accepts that language L and then write the sequence of moves done by the TM when the input sequence is $w = abbcbba$ so I had ...
-1
votes
1answer
61 views

Do these languages both have DPDA? [closed]

We have these languages: $$L_1 = \{a^nb^na^mb^m \ | n \ge 0, m \ge 1\}$$ $$L_2 = \{a^nb^na^mb^{2m} \ | n \ge 0, m \ge 1\}$$ are both these languages NCFG? I guess that both of them are NCFG because ...
0
votes
1answer
384 views

Pushdown automaton for complement of $L = \{ ww \mid w \text{ in } (0,1)^*\}$

I want to be able to describe the idea behind the pushdown automaton (no tables or diagrams). So, I already know that $L = \{ ww \mid w \text{ in } (0,1)^*\}$ is not context free. Since CFL are not ...
0
votes
1answer
301 views

Can a Turing Machine decide only non-regular languages?

I have an assignment where i need to create a Turing machine that decides an infinite language $L\subset \{0,1\}^*$ for which all $L'\subseteq L$, if $|L'|=\infty$, then $L'$ is not a regular ...
2
votes
3answers
369 views

Turing machine for $a^i b^j$ with $i \geq j$

I would have a brief question about how to construct a Turing machine that is accepting only this language: $\qquad\displaystyle L_2 = \{a^i b^j \mid i \geq j \}$. I can't come up with any mechanism ...
1
vote
2answers
229 views

Context-free grammar for language with unequal numbers of a and b

I've been trying to get a CFG for the language of all words with unequal numbers of a and b, i.e. $\qquad \displaystyle \{u \in \{a, b\}^* \mid \text{number of occurrences of $a$ and $b$ in $u$ are ...
3
votes
1answer
106 views

Abstract machine that can recognize repetition

Let $C$ be an infinite set of characters. I'd like an abstract machine which can recognize sequences consisting of $k$ (constant) of repetitions of a char from $C$. For example, if ${x,y,z} \subset ...
0
votes
1answer
47 views

Deciding the class of certain languages [closed]

I am preparing for my exam in Formal languages and Automata theory and I'm looking at some old exam questions right now. I need help with the following question: For each of the following ...
3
votes
2answers
592 views

Constructing a PDA for the language $\{a^m b^n : m < 2n < 3m \}$

I'm having a lot of trouble constructing a PDA for the language: \begin{equation*} \{a^m b^n : m < 2n < 3m \} \end{equation*} I know if I push a symbol for each $a$ I see, then pop 2 symbols ...
1
vote
1answer
64 views

Proving a PDA with CFG Transitions recognizes Context Free Languages

I'm working on a proof that deals with a modified PDA, which is identitical to a PDA, but with transitions: \begin{equation*} a,b \to c \end{equation*} where $a$ is a context free grammar, instead of ...
2
votes
0answers
64 views

Example of execution fragment of multi-process transition system

Here is a simple transition system of beverage vending machine: The exemplary execution fragments can look like this: Now, imagine we have multi-process TS where processes are identical and ...
0
votes
2answers
436 views

DFA/NFA/ε-NFA: subsetting each other or different sets?

I know that an ε-NFA (NFA with epsilon transitions) is not an NFA or a DFA and an NFA is not a DFA. HOWEVER, say you have a complete DFA. Isn't that theoretically an NFA and an ε-NFA? Just because it ...
0
votes
1answer
43 views

Reducing states of a GTG

I used this generalized transition graph with 3 states and got an equivalent generalized transition graph with 2 states: GTG: Equivalent with 2 states: I'm not sure about the regular ...
2
votes
1answer
56 views

Regular Expression as basis for creating this grammar

I made a right-linear grammar from a regular expression: The alphabet is: $Σ = \{a, b, c\} $ Regular expression: $r = cc^{*}(ba)^{*}bb$ My solution, it seems a little too short like I'm leaving ...
0
votes
2answers
197 views

Fundamental algorithms in formal language-automata theory [closed]

I'm willing to take a course in formal languages and automata theory , where we will explore side by side a functional programming language to implement the different algorithms we will encounter ...
5
votes
3answers
195 views

Bridge theorems for group theory and formal languages

Is there some natural or notable way to relate or link math groups and CS formal languages or some other core CS concept e.g. Turing machines? I am looking for references/applications. However ...
6
votes
1answer
176 views

For what kinds of languages is min |NFA| = Ω(min |DFA|)?

Consider a regular language $L$. Let $D(L)$ be a minimal DFA for $L$ and $N(L)$ be a minimal NFA for $L$ (minimal in the sense of the smallest possible number of states for an automaton that ...
2
votes
1answer
223 views

DFA drawing for binary string with substrings of minimum length 3 with at least two zeroes in each substring

In trying to gain a better understanding of finite state machines, I stumbled across this idea and have been confused as to how to approach this case in terms of a DFA. The set of binary strings ...
8
votes
1answer
133 views

What is the complexity of the emptiness problem for 2-way DFAs?

I'm wondering, what is the time-complexity of determining emptiness for 2-way DFAs? That is, finite automata which can move backwards on their read-only input tape. According to Wikipedia, they are ...
6
votes
2answers
115 views

Push Down Automatons “guess” - what does that mean?

I realize non-deterministic pushdown automata can be an improvement over deterministic ones as they can "choose" among several states and there are some context-free languages which cannot be accepted ...
6
votes
3answers
205 views

Algorithm to shrink a DFA by introducing nondeterminism?

This is somewhat related to another question I asked, but I feel it's different enough to warrant its own question. I'm doing research where I'm trying to find the structure of complements of a ...
4
votes
3answers
149 views

Are there algorithms to exactly minimize NFAs which are sometimes efficient?

I'm doing some research with NFAs, and I'm wondering there are algorithms which quasi-efficiently minimize them. I realize that this problem is $PSPACE$ hard, so I'm not looking for a polynomial time ...
5
votes
1answer
137 views

Reference request: proof that if $L \in DCFL$, then $L \Sigma^* \in DCFL$

So, it's fairly easy to prove that if $L \in DCFL$, then $L \Sigma^* \in DCFL$. Basically, you take the DPDA accepting $L$. You remove all transitions on final states, and then for each $a \in \Sigma$ ...
7
votes
1answer
136 views

Paper with proof that $L=\{ a^n b^n \mid n \geq 0 \} \cup \{ a^n b^{2n} \mid n \geq 0 \}$ is not Deterministic Context Free?

These lecture slides sketch a proof that $L=\{ a^n b^n \mid n \geq 0 \} \cup \{ a^n b^{2n} \mid n \geq 0 \}$ cannot be accepted by any Deterministic Pushdown Automaton. Unfortunately, the slides give ...
7
votes
1answer
125 views

Is the universe problem for one-counter automata with restricted alphabet size undecidable?

Consider the following universe problem. The universe problem. Given a finite set $\Sigma$ for a class of languages, and an automaton accepting the language $L$, decide if $L=\Sigma^*$. In [1], ...
3
votes
1answer
119 views

What does it mean to say that a language is “effectively closed” under an operation?

I've been reading some formal language theory papers, and I've come across a term that I don't understand. The paper will often refer to a set being "effectively closed under intersection" or other ...
6
votes
2answers
106 views

Classes of NFAs which allow efficient subset testing or unambiguity conversions

I'm doing some research regarding NFAs and inclusion problems with them. I know that in general, the inclusion problems, and converting to an unambiguous NFA, are both PSPACE-complete. I'm wondering, ...
2
votes
2answers
349 views

Designing a PDA w/o $\epsilon$-moves and $\leq 2$ states to accept an $\epsilon$-free CFL by final state

I understand that any CFL can be accepted by a PDA by final state or empty store but I have been rather stumped by this question. The question states that the PDA has at most 2 states. Clearly 1 will ...
4
votes
2answers
219 views

Why is the following language not context-free?

$L = \{a^n b^m | m \not= n^2 \}$ I guess I need to use Pumping Lemma for CFL in order to prove this. But I'm stuck. Assuming that $ a^n b^m = uvxyz$, we know that $v$ or $y$ can not have both $a$ ...
0
votes
1answer
425 views

How to generate a pushdown automata for accepting a language?

I have an exercise in my book to come up with a pushdown automaton accepting a language. The exercise is to come up with a state diagram for the PDA accepting the language of all odd-length strings ...
4
votes
2answers
380 views

Can a two-stack PDA accept language $a^nb^mc^nd^m$ which is not context-free?

Can a two-stack PDA accept language $L=\{a^nb^mc^nd^m \mid n \geq m\}$, which has no context-free grammar? I don't believe this has a context-free grammar, but please correct me if I'm wrong.
5
votes
3answers
388 views

Star free language vs. regular language

I was wondering, since $a^*$ is itself a star-free language, is there a regular language that is not a star-free language? Could you give an example? (from wikipdia) Lawson defines star-free ...
7
votes
1answer
141 views

Is there a strictly non-deterministic one-counter language whose complement is one-counter?

Let $A= \{L \mid L \;\text{is one-counter and \(\bar{L}\) is also one-counter} \}$ Clearly, $\text{Deterministic one-counter} \subseteq A$ Is it the case that $ A = \text{Deterministic ...
4
votes
2answers
53 views

Formal Language Syntax

Here is the question: Show that $L = \{0^m1^n : m > 1, n > 1, n < m \}$ is not regular. I am not sure what superscripts mean in this situation? Does it mean something like this: $0^5 = ...
1
vote
1answer
134 views

Is The Following Language Regular? [duplicate]

Let $L_{1}$ and $L_{2}$ be 2 languages over the same alphabet $\Sigma$. $$A(L_1,L_2)=\{x\in \Sigma^*|\exists y,z\in L_2\text{ such that } yxz\in L_1\}$$ Assume that $L_{1}$ is regular and $L_{2}$ ...
1
vote
3answers
6k views

How can $ww = www$ hold for any word $w$?

Speaking in terms of automata and regular languages, how would it be possible for a string repeating some $w$ twice equal a string repeating that same $w$ thrice? That is, why is the language $\qquad ...
3
votes
2answers
489 views

Prove that the language of unary not-prime numbers satisfies the Pumping Lemma

Here is a question from Daniel I. A. Cohen's book Introduction to Computer Theory: Consider the language: $\quad \mathrm{PRIME}' = \{ a^n \mid n \text{ is not a prime} \} = \{ \varepsilon, ...