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

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Is the language $L$ generated by 'Fibonacci Strings' (as given in the desciption) regular? If not, disprove by Pumping Lemma

The Fibonacci strings are defined as follows: $S_1=a$, $S_2=b$ and $S_k=S_{k-1}S_{k-2}$ for $k>2$ . For example $S_3=ba$ , $S_4=bab$ etc. Let $L$ be the language generated by the Fibonacci strings. ...
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0answers
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Can we build a DFA less than 5 state for word length 4( 1100)? [on hold]

========================================================== 1 if possible kindly, help me with this question.
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2answers
25 views

What are good techniques for creating a DFA state diagram given a set of accepted/rejected strings?

I am in a Discrete Structures class and my teacher is pretty big on proving his intellect to the class and getting an average of about 60% for his test questions. Right now we are working with ...
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0answers
23 views

NFA that accepts binary strings starting with 1 and with at least 01, or at least 010, or both. [closed]

Im not sure if I am understanding this question correctly. Its a problem without a solution in my text. Starting with 1, and at least 01 or at least 010 or both these substrings..... So a regular ...
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1answer
20 views

Is dead state only linked with the final state in any automata?

I am very much new to this subject and as far as I have tried the small research I found this most meaningful at this link Dead State - A rejecting state that is essentially a dead end. Once the ...
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1answer
55 views

Boolean formulas over omega automata

I've been reading on omega automata(automata on infinite words) and stumbled upon a definition involving logic which caught me off guard. For example, on Buchi automata the definition I originally ...
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2answers
47 views

Prove that $R_1 \times R_2$ is a regular language for $R_1, R_2$ regular [closed]

Let A and B be two sets. The cross products of A and B are defined as : AxB={(a,b): a belongs to A and b belongs to B }. Assume R1 and R2 are regular languages over an input alphabet Σ={a,b}. Prove ...
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0answers
24 views

Inequality for the set of factors of length $n$ of some regular language

If $W \subseteq X^*$ is some language denote by $$T(W) := \{ u \in X^* : \mbox{there exists }x, y \mbox{ such that } xuy \in W \}$$ the set of factors (infixes) of $W$. If $W$ is regular, then ...
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2answers
27 views

Set of all factors of regular language regular?

If $L$ is a regular language (i.e. acceptable by a finite automata), is the the set of its factors (infixes) also regular?
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2answers
44 views

Can finite automata keep track of history or relevant history?

I am unable to understand that if I have a Finite automaton which say accepts all the strings that end with ab, now if input given is "aab" now it reads 'a', then it reads second 'a',this implies ...
2
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2answers
49 views

Finite automata as dynamical systems

In abstract (deterministic finite) automata theory the set of states of an automaton is an arbitrary set Q, and the transistion function is a specific set δ ⊆ Q × Σ × Q (with alphabet Σ, i.e. another ...
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0answers
56 views

Does a mathematical construct exists which explains all theories?

If I am not wrong quantum mechanics is about measurements of different physical properties and probabilities of getting different outcomes. We have a mathematical construct to explain it, that is how ...
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2answers
95 views

Describe and count the set of sequences containing $20$ or $02$

Let $X = \{ 0,1,2 \}$ be a ternary alphabet and denote by $X^*$ the set of finite sequences (i.e. strings) with three symbols. For $w \in X^*$ with $n$ the length of $w$ and $w = w_1 w_2 \cdots w_n$ ...
2
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1answer
49 views

DFA/NDFA problems confirmation

Im studying for a test on my own and have been working through some previous test questions. Can anyone help me confirm that the answers I've gotten for the problems below are correct or not. If there ...
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2answers
34 views

How to design a finite state automaton that recognises the languages like $1^n 0^n$

The question goes like this: Design a finite state automaton that accepts binary strings with at least two $0$s and at most two $1$s. I can easily design an NFA which accepts at least two $0$s OR at ...
2
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2answers
33 views

Is the language $\{yxzx^Ry^R \mid x,y,z \text{ belongs to } \{0,1\}^+ \} $ regular?

This is a question from Iran's national grad school entrance exam. In the answers key, the answer was that the following language is regular but I doubt it is true, I proved using pumping lemma that ...
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2answers
56 views

Number of finite-state machines with $n$ states, output alphabet size $a$, and binary input

How many FSMs are there where the machine has $n$ states, reads a binary symbol at each time-step, and may or may not output a symbol from an alphabet of size $a$ after each transition?
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1answer
21 views

is language accepted by finte state automaton

Hi I need to prove these languages are accepted or not by the following finite state automata. for 1 does this mean that we need an even number of a's or that a is literally 2,4,6,8....etc also ...
2
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1answer
37 views

Why is this language not regular?

I am studying Automata using the Coursera course created by Jeff Ullman. On slide 36 of this presentation: http://spark-public.s3.amazonaws.com/automata/slides/3_fa2.pdf it says that the language is ...
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1answer
23 views

How to simulate a 3-stack automaton with a 2-stack automaton?

Since a 2-stack automaton is Turing-equivalent, it is possible to simulate a 3-stack automaton with just a 2-stack automaton. But how so? How it is normally done?
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3answers
172 views

Number of states in a finite automaton

How many states are required by a deterministic finite automaton to store $m$ words each of length $n$? I came across $2^{mn}$ as the solution but there was no explanation.
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1answer
40 views

Is the Champernowne constant an automatic number?

The Champernowne constant in base $b \geq 2$ is obtained by concatenating the $b$-ary expansion of every integer. For example, in base $10$ this is $$ 0.123456789101112131415\dotsc $$ Question: Is the ...
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1answer
22 views

Why Petri Net tokens are not added?

Reading this article it says: A firing of an enabled transition removes one token from each input place and adds one token to each output place. Now if I have the following net, with all ...
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0answers
11 views

inverse proof of closed under union

I am being posed the following question: given are languages $L_1, L_2, L_3 $ and $ L_4$. $L_1$ is a decidable language and $L_2$ and $L_4$ are both recognizable languages. Considering $L_1 = L_2 ...
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1answer
44 views

How n (1+b) is not prime?

Here is the complete proof taken from this link How do I convince myself that n(1+b) is not prime when b>=1? Here is what I did: if n is 3 and b is 3. Then ...
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2answers
28 views

Why is the below language regular?

If I have a language $$L=\left\{wxwy : w,x,y \in \{a,b\}^+ \right\}$$ I am not getting how come we are able to write regular expression for this of the form $$a(a+b)^+ a(a+b) ^+ + b(a+b)^+ b(a+b) ...
2
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1answer
29 views

pumping lemma for CFL vs pumping lemma for regular languages

Is the pumping lemma for context free languages a generalization of the pumping lemma for regular languages (for instance if we set $u=\epsilon, v=\epsilon$ we can then relate $wx$ in the pumping ...
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1answer
62 views

Quick question on DFA

I'm asked to list all DFA over the alphabet sigma = {0} such that the set of states is {s0, s1}, for which the initial state is s0 and the set of accept states is either {s0} or {s1}. And also asked ...
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1answer
28 views

Best approach to determine the equivalence classes of a formal language

I created a minimum automaton for a formal language using the Myhill-Nerode theorem. The language for which I created the automaton is defined by $L=\{w \in \{a,b\}^*:w=av \text{ for a word } v ...
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0answers
34 views

Construct PDA that accepts the language $ L = \{ w \in \{ a,b,c\}^*; |w|_c=|w|_a + |w|_b \} $

Problem Construct PDA that accepts the language $ L = \{ w \in \{ a,b,c\}^*; |w|_c=|w|_a + |w|_b \} $ My first idea was this: There can be an "a","b" or a "c" at the beginning of a word Then we ...
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2answers
30 views

How to draw a DFA for complement of a regular language using a regular expression?

How can I draw an FA for the complement of the language $L(r)$? $L(r) = a^* (aba^*)^* b^* a^*$ I can draw an FA for $L(r)$ and convert to DFA and then take the complement, however it seems very long ...
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2answers
44 views

Proving that $L := \{a^n\mid\exists k \geq 0\ n = k^3\}$ is not a regular language

I'm having trouble using the pumping lemma to prove this language $L := \{a^n\mid\exists k \geq 0\ n = k^3\}$ is not regular. Assume $L$ is regular. Thus there is a DFA $M$ for it. Choose $m$ as the ...
2
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1answer
30 views

Concatenation of Finite Languages and Regular Languages

I know that the following statements regarding Concatenation are false. However, I'm having difficulty explaining why they are false with simple counter-examples. I'm able to find simple ...
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1answer
80 views

Why are Recursively enumerable languages closed under intersection?

when Recursively enumerable sets are not closed under complement ,then how come they are closed under intersection because the definition of intersection comes as L1 intersection L2= complement(L1' ...
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2answers
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Is the intersection of a finite language and an infinite language always a regular language?

Is the intersection of a finite language $L_1$ and an infinite language $L_2$ always a regular language? I've tried a few examples and the result always seems regular. $\{\} \cap a^nb^n = \{\}$ ...
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1answer
37 views

Context-free language or not

It is language: $L = \left\lbrace a^ib^jc^kd^l \mid i+k < j+l+3 \right\rbrace$ Is it context-free or not? I have two versions: 1)Pumping lemma(refute): get a word $uvxyz = aabcd$ if $i=2$ we get ...
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1answer
26 views

Minimum Size of DFA

I'm confused about the following DFA problem: Let L denote the set of all strings in $\{a, b\}^∗$ that contain abb or aab as a substring. Show that any DFA that decides L must have at least five ...
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1answer
22 views

Proving from Myhill-Nerode that the minimum DFA is the smallest automaton recognizing $L$

From this paper, In the proof of (Myhill-Nerode theorem) it's stated that if $L$ is a regular language and the index of $\sim_L$ is $i_L \in \mathbb{N}$ then it's both necessary and sufficient for ...
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1answer
55 views

Context free grammar $\{a^n b^m c^k\; : \;k>m \; \; k>n\}$

Is this a CFL? $$\{a^n b^m c^k\; : \;k>m \; \; k>n\}$$ When on seeing $a$'s and $b$'s I push them onto stack and as I see $ c$ as input if $ TOS$ is $b$ ,I pop them ,again if $TOS$ is a,I pop ...
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1answer
38 views

Construct a deterministic finite state automaton

Construct a deterministic finite-state automaton that recognizes the set of all bit strings that end with 10. This is what I drew. Not sure if its correct. State 2 is the final state. Am I missing ...
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1answer
20 views

Find the language recognized by the given deterministic finite state automaton

I got 01* U 1(01)01 as my answer. I'm not sure if its right.
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0answers
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4th case in Ogden's Lemma

I'm trying to understand Ogden's Lemma and I know there are four cases, but in the next example I can only find 3: A = {$0^n1^m0^k$ | k = max{n,m}} is not context free: Assuming: z = $0^k1^k0^k ∈ A$ ...
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1answer
27 views

How to find the right quotient of a language given two languages?

If $L_1= \{a^n b^m \mid n \geqslant 1, m \geqslant 1 \} \cup \{ba\}$ and $L_2= \{b^m \mid m \geqslant 0 \}$. I am not getting how the DFA for $L_1/L_2$ is constructed in the second figure ...
2
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1answer
43 views

Designing a Turing Machine - low level transitions

I couldn't figure out how to proceed with this question. Preparing for the finals, can someone explain how to do this step by step? Design a TM, write low level transitions for $\{a^i b^j :i ≤ j ≤ ...
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1answer
32 views

Let $LOOP_{TM}$ be descriptor language of all touring machines that won't halt for any input. Show reduction of $HALT_{TM}$ to $LOOP_{TM}$

Question from Homework that I'm having difficult to answer on: Let $LOOP_{TM} = \{\langle M\rangle \mid \text{M is a TM that does not halt on any input w}\}$ Let $LOOP_{TM}$ be descriptor ...
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2answers
42 views

Converting an NFA to DFA

I am atttempting to convert an NFA into an equivalent DFA. I did it, but i am not sure if it is correct. If anyone can please take a look at let me know if it is correct or if there is something wrong ...
2
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1answer
19 views

Finding regular expressions for which a given Turing machine halts and accepts, halts and rejects, and diverges.

Consider the Turing machine M = (Q,Σ,Γ,δ,q,F) F = {t} Q = {q,r,s,t,v,x} Σ = {a,b,c} Γ = {B,a,b,c} δ = [q,a,q,a,R] [q,b,q,b,R] [q,c,v,b,R] [q,B,r,B,L] [r,a,s,B,L] [r,b,s,B,L] [r,c,s,B,L] ...
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1answer
29 views

Graph and language/automaton equivalence

I'm looking for a reference rather than an answer. I think I'm just not Googling the right combination of terms. I imagine that there is a class of graphs which is equivalent to some class of ...
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2answers
19 views

Languages and their Regular Expressions - Automata

I am working on some Automata practice problems. I am working a 2 part question. Here it is: Let $\Sigma = \{a,b\}$ be an alphabet. Let $L = \left\{w \in \Sigma^* \mid n_a(w) \le 4\right\}$ ...
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1answer
32 views

Pumping Lemma proof and the union/intersection of regular and non-regular languages

I am still learning the pumping lemma. I have a problem for which I used it. I used it on the first part (a) but I am unsure if it is correct. Parts b-d, I am not sure how to do it. I created a dfa ...