Questions tagged [nondeterminism]

Questions about automata, formal grammars or other computation-models that specifically relate to the use of nondeterminism. Not to be confused with randomness or ambiguity!

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12
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3answers
21k views

How does an NFA use epsilon transitions?

In the picture below, I'm trying to figure out what exactly this NFA is accepting. What's confusing me is the $\epsilon$ jump at $q_0$. If a $0$ is entered, does the system move to both $q_0$ and $...
5
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1answer
153 views

Is there $L$ such that $L$ and $\bar L$ are context free, but $L$ is not deterministic context free?

The usual candidates for context free languages whose complement is also context free, but they are not regular are the Deterministic Context Free Languages ($DCFL$). For example, $L=\{a^nb^n\mid n\...
1
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1answer
302 views

Why is it that the transition function for DPDA's only works for 1 alphabet symbol, and 1 stack symbol?

Why is it that the transition function for DPDA's only works for 1 alphabet symbol, and 1 stack symbol? Say f is the transition function, why does having ...
1
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1answer
69 views

Space penalties for the simulation of a non-deterministic Turing machine by a single-tape deterministic Turing machine

If I have some non-deterministic Turing machine $NDTM$ running some process $Q$ and I wish to simulate the same process $Q$ with a deterministic single-tape Turing machine $DTM$, there will of course ...
0
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1answer
180 views

Non-deterministic algorithm to check if a list has some given value

I know that I can build a non-deterministic algorithm with a CHOICE function that verifies if a value x is in an array in O(1) ...
5
votes
2answers
246 views

Using SMT solvers to generate random solutions to given predicate

I am interested in generating random solutions to predicates. I only need SMT for integers with the following predicates/functions <, >, <=, >=, ==, !=, +, * The algorithm I want should produce ...
3
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1answer
158 views

The communication complexity of non-equality

I'm familiar with the fooling set technique to obtain lower bounds for communication complexity protocols. The most basic example is the equality function for which the diagonal matrix gives the ...
2
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1answer
4k views

NFA - string acceptance (decision problem) test

I am interested in testing for a given string (w) whether it is in the language (L) defined by a nondeterministic finite automaton (A). I have some blurry point in my mind. What is the complexity of ...
3
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2answers
562 views

Are nondeterministic algorithm and randomized algorithms algorithms on a deterministic Turing machine?

An algorithm on an abstract machine is a finite sequence of operations of the machine. (Correct me if I am not correct.) However, there are different kind of algorithms, such as deterministic, non-...
8
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1answer
3k views

Are DCFLs closed under reversal?

According to this chart, DCFLs are closed under reversal. However, I am not convinced as the intuitive proof (reversing the arrows of the controlling finite state machine and switching the pushes and ...
0
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1answer
69 views

NFA state complexity for the complement of EPAL restricted to a fixed length

I've been having trouble proving the next statement: Let $L_n=\{ww, |w|=n\}$ (the set of equal-length palindromes (EPAL) restricted to length $2n$). Prove that $L^c_n$ can be accepted by an NFA ...
1
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0answers
547 views

K -> 2 tape reduction for nondeterministic Turing machines

How to I show that any language in NTIME(T(n)) can be accepted by a non-deterministic 2-tape O(T(n)) time-bounded Turing machine, with modifiable input tape? I've seen the k to 2 tape reduction for ...
2
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2answers
571 views

Algorithms which are both deterministic and non-deterministic

I'm just starting my second year in computer science and one of my classes briefly touched upon deterministic vs. non-deterministic algorithms. This got me thinking - is there any use for algorithms ...
4
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1answer
443 views

Given a non-deterministic Mealy machine $M$, if $L$ is regular, is $M(L)$ regular?

Consider a nondeterministic Mealy machine, $M$, defined as follows: $M = (Q, \Sigma, \Delta, \delta, \tau, q_0)$ where $Q$ is a finite set of states $\Sigma$ is an input alphabet $\Delta$ is an ...
-1
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1answer
59 views

Why is there still nondeterminism in my automaton?

I've been solving some exercises recently and it appears my answer was wrong for this particular example. The task is to convert this NFA into a DFA: My attempt is this: Now the tool I'm using (...
8
votes
2answers
888 views

Counting the number of words accepted by an acyclic NFA

Let $M$ be an acyclic NFA. Since $M$ is acyclic, $L(M)$ is finite. Can we compute $|L(M)|$ in polynomial time? If not, can we approximate it? Note that the number of words is not the same as the ...
7
votes
1answer
225 views

Smallest NFA accepting concatenations of two words of the length $k$ which are different at all positions

Let $k\in \mathbb N$ I'm looking for a small NFA build for the language of concatenation of two words of the length $k$ which are index-wise different, i.e. $$L_k=\{u\cdot v \in \Sigma^* : |u|=|v|=k\...
2
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3answers
4k views

Problem understanding DFA & NFA equivalence in Theory of Computation

Before asking this question,I had gone through Equivalence of NFA and DFA - proof by construction but my question is a bit different from that. I was reading Michael Sipser's ...
0
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4answers
207 views

How is a nondeterminisitic automaton running on an input?

A nondeterministic automaton, after reading an input symbol at some state, may jump into any of a (finite?) number of states. Does the automaton uniformly randomly choose one out of the several ...
1
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2answers
415 views

Is there a software algorithm that can generate a non-deterministic chaos pattern?

Is there a software algorithm can generate a non-deterministic pattern or sequence? In Chaos theory, simple processes can create deterministic patterns, and psudo-random number generators can generate ...
4
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1answer
155 views

Upper bounds for $NP$ based on $NEXP = EXP$

It's open whether $EXP = NEXP \to P = NP$ (the other direction can be shown by padding). My question: has there been any progress along these lines at all? For example, can we show that $EXP = NEXP \...
1
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2answers
52 views

NDFA associated with language L

Let A = $(Q, \Sigma, \delta, S, F)$ be a deterministic finite automaton associated with the language $L \subseteq \Sigma^*$ $L' = \{y \in \Sigma^*:\exists x\in L. |x| = |y|\}$ $L \subseteq ...
-3
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2answers
801 views

Why it is said that LBA is a non deterministic Turing Machine

I have read that linear bounded automaton is a Non deterministic Turing machine. Why is it so?
23
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10answers
7k views

Why is non-determinism a useful concept?

An automaton is an abstract model of a digital computer. Digital computers are completely deterministic; their state at any time is uniquely predictable from the input and the initial state. When we ...
2
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1answer
1k views

Why Deterministic PDA accepts $\epsilon$ input but DFA not

I was going through a deterministic PDA that accepts $wcw^R$ (described in Ullman's textbook), in which the last transition is given as $(q_1,\epsilon, Z_0)\to(q_2,Z_0)$, where $q_2$ is the final ...
-1
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1answer
118 views

A NPDA for the language $L = \{w \mid w \in \{a,b,c\}^*, n_c(w) = n_a(w) + n_b(w)\}$

Consider the language $L = \{w, w \in \{a,b,c\}^*, n_c(w) = n_a(w) + n_b(w)\}$, where $n_q(\omega)$ is defined to be "the number of $p \in \omega$. I have tried a couple of PDA's that follow this ...
9
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1answer
693 views

Why is this function computable in $O(n^{1.5})$ time?

My textbook says: "We define the function $f\colon \mathbb{N}\to\mathbb{N}$ as follows: $f(1)=2$ and $f(i+1)=2^{f(i)^{1.2}}$. Note that given $n$, we can easily find in $O(n^{1.5})$ time the number $i$...
4
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1answer
5k views

Creating a Deterministic Push Down Automata

I saw this old post on stack overflow of a PDA that accepts a language where there are exactly twice as many a's as there are b's. The image they used is below and so is the link to the post itself. ...
1
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2answers
86 views

2 threads accepted at the same time [closed]

Assuming we have an automaton that simultaneously accepts a string on two paths. Would this mean that the construction of the NFA might be faulty? In other words; at the end of any string over any ...
0
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0answers
36 views

Non-deterministic finite state automoton [duplicate]

I am taking a course in the theory of computation and am trying to understand how to correctly design NFA's so that I can transform them into regex. I was wondering if I have Sigma={a,b} and need to ...
5
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3answers
11k views

Decidable languages kleene star closure - question on a proof

I read a proof on the closure of decidable languages under kleene star. It begins by saying that the turing machine we want to find would non-determistically split the input string and then use the ...
2
votes
1answer
2k views

how to solve NFA acceptance problem in polynomial time

I need to show that the language Anfa = {(A,w)| A is an nondeterministic finite automata that accepts w} can be decided in polynomial time. My problem is every solution that I think of requires ...
3
votes
3answers
462 views

Relaxing the stack in a push down automata

Given a non-deterministic push down automata (we define "accept" here using accept states), if we assume any operation popping from the stack and checking if the top of the stack contains some symbol ...
1
vote
1answer
322 views

NFA for right left multiplication

Given the following multiplication table how could one construct an NFA such that it accepts all strings that have a certain product (say a) ? The string "abcb" would be evaluated as (a(b(cb))) = a ...
-2
votes
2answers
125 views

help with the probability of acceptance of a Nondeterministic Pushdown automata

I have this nondeterministic pda: $$\Sigma= \{a,b,c\}$$ and $$ L=\{\omega\ \epsilon\ \Sigma^*\ |\ \omega\ = \alpha\beta\beta^R\gamma\ and\ \alpha,\beta,\gamma\ \epsilon\ \Sigma^*\ and\ |\beta|\ &...
2
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1answer
2k views

NFA to DFA convertion explanation

I've converted this NFA to a DFA and I get a similar soultion automata but I'm not sure if I really understand everything. Please correct me if I'm explaining it wrong, I would love some feedback. ...
1
vote
1answer
11k views

Maximum number of states in minimized DFA from NFA with $n$ states [duplicate]

If an NFA with $n$ states is converted to an equivalent minimized DFA then what will be the maximum number of states in the DFA? Will it be $2^n$ or $2n$?
1
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2answers
1k views

Determining Length of a walk in Nondeterministic Finite Automata with Lambda Transitions

I am learning about CS Theory and specifically Nondeterministic Finite Automata (NFA) right now. In my book I came across a section of text that discussed a way to determine the length of a walk ...
5
votes
3answers
3k views

What does “deterministic” mean in the context of memory management?

At the time of writing, Wikipedia describes determinism as: "a deterministic algorithm is an algorithm which, given a particular input, will always produce the same output, with the underlying ...
8
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3answers
746 views

Why do most scientists believe that P≠NP?

I read that most scientists don't believe that P=NP. It might be subjective but can you simplify why not? I'm not informed enough to have an opinion but I'd like to know the definitions and some "...
14
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4answers
616 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 ...
8
votes
3answers
386 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
356 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 ...
4
votes
1answer
812 views

Checking whether a digraph on $n$ vertices contains exactly $10\sqrt{n}$ strongly connected components in NL

I am studying now for a test in my complexity course. When I solved previous exams I saw the following question: Prove that the language $L$ of all directed graphs on $n$ vertices that contain exactly ...
14
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3answers
6k views

Why is NFA minimization a hard problem when DFA minimization is not?

I know that we can minimize DFAs by finding and merging equivalent states, but why can't we do the same with NFAs? I'm not looking for a proof or anything like that--unless a proof is simpler to ...
8
votes
1answer
321 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 ...
5
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1answer
199 views

Nondeterministic finite state machine without any initial state possible

Is it theoretically possible to have a nondeterministic finite state machine without any initial state or does it need at least one initial state?
7
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1answer
16k views

Converting an NFA to regex using GNFA algorithm?

So I've been trying to crack this for a long time and almost feel like I am going in loops about this question. Given the following NFA: Using the GNFA algorithm get the regular expression. I ...
7
votes
2answers
211 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
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1answer
483 views

what is glushkov NFA. What is the difference between Glushkov NFA and Thompson NFA?

I saw this term "Glushkov NFA" at http://lambda-the-ultimate.org/node/2064 . Search engines are returning references to articles that use glushkov nfa, but nothing specific about the glushkov nfa ...