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!
269
questions
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How to prove Shortest Common Superstring is NP-Hard
After some research and many youtube videos I have learnt that to prove a problem is NP-Hard; you would need to reduce that problem to known NP-Hard problems such as Subset Sum Problem, Halting ...
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0answers
6 views
Push Down Automatas: Is it still an accept state if stack is not empty?
I'm currently seeing if a PDA is in an accept state give an input string. After reading the entire input tape, I am currently in the accept state.
However, in the stack, there are two items in it.
So ...
2
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1answer
65 views
If A and B are NP-complete, then A ∪ B need not be NP-complete
I am studying the proof of this exercise (link)
There exist N P-complete languages A and B such that A ∪ B is not N P-complete. Example:
$A = \{1x : x ∈ SAT\} ∪ \{0x : x ∈ \{0, 1\}^∗\};$
$B =...
1
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1answer
28 views
Converting non-deterministic algorithm to deterministic
I was thinking about an non-deterministic algorithm to generate all the subsets of the $\{1..n\}$ set.
...
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1answer
88 views
How to prove Exact cover problem is NP Complete using Vertex Cover problem?
Using reduction theorem in NP, we want to prove that Exact cover is NPC by reducing it from Vertex Cover Problem. It is easy to derive it from SAT, but we can't find a solution yet to derive it from ...
4
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1answer
314 views
How to determine if a language is deterministic context-free language?
I have the following question to solve : DCFL means Deterministic Context-Free Language.
Let $L$ be a DCFL over an alphabet $\Sigma$. For each of the following functions of $L$, determine whether $...
3
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1answer
52 views
motivation and idea of defining non-deterministic Turing machine
This is a very basic question but I spent some time reading and find no answer. I am not computer science majored but have read some basic algorithm stuff, for example, some basic sorting algorithms ...
0
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1answer
61 views
NFA for all strings not containing 1010
if I want to design a NFA (that's NOT A DFA) that accepts the set of all strings that do not contain the substring 1010, is this correct? because I can just accept 1010 by capturing it in the starting ...
2
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0answers
29 views
Minimal regular expression from minimal NFA for finite language in polynomial time?
Given a minimal NFA for a finite language, is there a polynomial-time algorithm to find a minimal regular expression for the same language?
This question is based on a recent question regarding ...
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0answers
50 views
Why is it not possible to prove the equivalence of nondeterministic and deterministic Turing Machines the same way as for NFAs and DFAs?
I found en excercise asking this question.
I know that for proving the equivalence of NFAs and DFAs we can use the conversion through subsets, and that for proving the equivalence of nondeterministic ...
2
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1answer
52 views
Like transitive reduction, but removing vertices rather than edges?
Suppose I have a directed graph $G = (V, E)$ (or, which is the same, a relation on the set $V$ as defined by the adjacency matrix) that may contain three vertices $x, y, z$, such that $xy, xz, yz \in ...
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1answer
38 views
How to make Turing machine deterministic?
My Turing machine starts with an empty tape. It writes a random word of the set $0^n1^n$ to the tape. Hopefully i made no mistakes.
My question is about the productions coming out of state $q_0$:
$δ(...
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1answer
50 views
What publication first introduced the concept of a non-deterministic Turing machine?
What publication first introduced the concept of a non-deterministic Turing machine?
Turing did not define the concept in his 1936 paper.
0
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1answer
42 views
TQBF PSPACE-COMPLETE : Why this algorithm is exponential but Savitch's not?
So this is a question pertaining to the proof for $PSPACE-COMPLETE$ (for TQBF for example). The idea is to first prove the $L$ $is$ $PSPACE$(easy part) and next is to prove $PSPACE-COMPLETE$. The ...
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1answer
35 views
Why does NTM need to derive certificate to prove “If a language is in in NP iff it is decidable by some nondeterministic polynomial time TM”?
(Sipser's Chapter 7: Time COmplexity, Pgs 294-295)
If we have to prove the forward direction, then we must have the certificate along with the verifier. I don't get why we are "guessing the ...
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2answers
79 views
Why is the run time of an $f(n)$ space decider bounded by $2^{O(f(n))}$?
In the proof of Savitch's theorem from the 3rd edition of Sipser's Intro to Theory of Computation, Sipser claims that the maximum time that an $ f(n) $ space nondeterministic Turing machine that halts ...
2
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2answers
33 views
Given an non-deterministic finite automaton, will its determinization always have unreachable states?
Given an NFA that accepts the regular language L, will its equivalent DFA which accepts the same language L always have unreachable states.
If it does, why?
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How to adapt proof of the ND time hierarchy theorem for alternate definition of NDTM?
For reference, the version of the nondeterministic time hierarchy theorem in question is this one:
The relevant portion of the proof in question (also from Arora-Barak) is here:
Arora-Barak define a ...
2
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1answer
38 views
NL problem? $CONN$= {$〈G,k〉$ ∶$G$ is undirected graph with at least k connected components}
Consider the following decision problems:
$CONN$= {$〈G,k〉$ ∶ $G$ is undirected graph with at least $k$ connected components}
$E-CONN$= {$〈G,k〉$ ∶ $G$ is undirected graph with exactly $k$ connected ...
1
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1answer
77 views
Is the halting problem solvable for NPDAs?
After the total silence in response to my last question, I am rethinking my assumptions. DPDAs are, of course, solvable, and I believe that their loops can be found in the manner I described in my ...
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1answer
1k views
Non-deterministic Finite Automata | Sipser Example 1.16
I am working through the Sipser Book (2nd edition) and came across this example, which I do not understand. In the book it states that this NFA accepts the empty string, $\epsilon$.
Could someone run ...
2
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0answers
78 views
Detecting loops in NPDAs
I'm aware that the halting problem is solvable for PDAs, but I have recently discovered that I am wrong about how to actually do it. I used to think that you could detect an infinite loop by meeting ...
3
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2answers
57 views
In what sense are dataflow architectures non-deterministic?
The Wikipedia article mentions non-determinism in the context of dataflow architectures. Arthur Veen's paper mentions non-determinism when it elaborates on MERGE nodes as conditional constructs.
Are ...
2
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1answer
38 views
Why “Choice Points” introduce non-determinism in a program?
I'm studying the didactic programming language Oz, following the book "Concepts, Techniques, and Models of Computer Programming".
In the book, the nondeterminism is introduced through the concept of ...
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1answer
159 views
What's the purpose of the non-deterministic Turing machine?
(*) Acronyms
NTDM := non-deterministic Turing machine.
TM := deterministic Turing machine.
(*) Consider the following idea
The NTDM is able to follow, in parallel, all paths of the tree of the ...
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2answers
124 views
Describe in words how a NTM can simulate a DTM
I have this assignment
Describe in words how a DTM can simulate a NTM
Describe in wordshow a NTM can simulate a DTM
I'm working on this request and I'm crushing with the comparison.
1-I ...
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0answers
34 views
Characterization of NFA whose equivalent (minimal) DFA has exponential number of states
(I don't know if there are standard names for this, so) Let's say that a Nondeterministic Finite Automaton (NFA) is $n$-expansive if it has $n$ states and any Deterministic Finite Automaton (DFA) ...
0
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0answers
70 views
Proving the Complement of a DCFL is DCFL [duplicate]
If I Have a DCFL $L$ ( a CFL which can be recognised by a DPDA ),
How do I prove that $\overline{L}$ is also a DCFL
I checked my textbook for a proof but I wasn't able to understand the language.
Can ...
3
votes
1answer
82 views
If $NP\subseteq DTIME[n^{O(\log n)}]$ then what happens?
If $NP\subseteq DTIME[n^{O(\log n)}]$ then what happens? Does it imply $NP\neq EXP$? Is there any other consequences such as $BPP\neq EXP$? Does it also give $PSPACE\subseteq DTIME[n^{O(\log n)}]$?
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2answers
95 views
Why cannot we enumerate all Turing machines that have no fixed point?
The language
$$
L_1 = \{w \in \{0, 1\}^\ast \mid \exists x \in \{0, 1\}^\ast\colon M_w(x) = x\}
$$
($w$ is an encoding of a DTM, $M_w$ is the respective DTM.)
is not decidable, according to Rice's ...
7
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0answers
82 views
Automata that is Turing complete if you add a nondeterminism
Pushdown automata have an interesting property: non-deterministic ones belong to a different computational class than deterministic ones. This is in contrast to finite state and turing machines, for ...
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1answer
94 views
How do I construct a NTM that accepts the language consisting of the coding of turing machines that halt on one input?
I currently have a problem with the following question:
Let $L = \{ \langle M \rangle \mid \exists w: \text{$M$ halts for $w$ in at most $|w|^3$ steps} \}$.
Construct an NTM (non-deterministic Turing ...
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votes
1answer
120 views
The definition of weakest precondition for a non-deterministic language
In the classical IMP language, the definition of weakest precondition is:
definition "wp c Q s ≡ ∃t. (c,s) ⇒ t ∧ Q t"
This is stating that from state s, after ...
3
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1answer
143 views
The Law of Excluded Miracle in the language of guarded commands
The definition of weakest precondition is familiar (let me use Isabelle's syntax here):
definition "wp c Q s ≡ ∃t. (c,s) ⇒ t ∧ Q t"
the weakest precondition ...
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2answers
450 views
What to do with empty set during NFA to DFA conversion?
I am currently converting this NFA to a DFA
I have come up with the following DFA:
...
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2answers
76 views
Understanding Hamiltonian Path, NP vs Co-NP
I am having difficulty understanding the distinction between NP and Co-NP.
According to my textbook (Sipser), the HAMPATH problem is in NP. That is, for the language: HAMPATH = { (G,s,t) | G is a ...
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1answer
698 views
PDA of the language where the number of a's are NOT equal to the number of b's
I have this NPDA for language L = {w: num_a(w) == num_b(w)}
all loops in q1
...
0
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1answer
58 views
Given a NP Algorithm for SAT, do we expect to have Correct and Incorrect Solutions?
I am reading about Boolean Satisfiability Problem and Nondeterministic Algorithms, in the latter defination it says :
In computational complexity theory, nondeterministic algorithms are ones that, ...
3
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0answers
40 views
What is the difference between the choice operator and nondeterminism in CSP?
I'm learning CSP now for my research. First time doing formal work in CS. I'm having a hard time understanding the difference between choice $\square$ operator and the nondeterminism $\sqcap$ operator....
2
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2answers
367 views
Why SAT Requires A Non-determinstic Algorithm?
I am getting started to understand the probelm of Satisfiability and i am reading (Computers and Intractability: A Guide to the Theory of NP-Completeness).
I do understand the difference between a ...
1
vote
1answer
412 views
How to implement a maximal munch lexical analyzer by simulating NFA or running DFA?
I'm planning to implement a lexical analyzer by either simulating NFA or running DFA using the input text. The trouble is, the input may arrive in small chunks and the memory may not be enough to hold ...
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2answers
620 views
Understanding $\epsilon$ transitions on NFA
I can't understand why $\epsilon$ is accepted. I thought if $\epsilon$ is inputed then it would go from $q_1$ to $q_3$. $a$ is also accepted, but I though if $a$ is inputed then then the NFA would die,...
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1answer
170 views
How do non-deterministic algorithms work on current machines?
I have some questions regarding the exact nature of non-deterministic algorithms. Is it right that non-deterministic algorithms do not rely on any randomness whatsoever? In which case, this Wikipedia ...
2
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1answer
45 views
In certificate view of NL can we force the guesses to be in some format like $a^n b^n c^n d^n$?
In certificate view of NL the size of our guess can be polynomial.Can this guesses be like $a^n b^n c^n d^n$. Can we force the guesses to be in some format? I think it(the format) can be in regex ...
0
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1answer
136 views
Drawing a NFA for a string
I have these grammar rules defined as follows,
FDL -> FDEF FDL | ε
FDEF -> #feature #: FEXP
FEXP -> #op #( FLIST #)
FLIST -> FEXP #, FEXP | #feature
...
1
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1answer
55 views
Can we call deterministic equivalent of all NFA to be finite
Finite automata is defined as a simple machine having small memory. A deterministic equivalent of a NFA with n states will have O(2^n) states,so the number of states grow exponentially. So can we ...
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1answer
62 views
What will happen if input is larger than required in a NFA
This is my first time in the field of TOC so I am not able to provide any self-approach while asking .In the above example what will happen if input string is "1001" or "1111"?The state q4 can be ...
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2answers
183 views
NP Class Definition of a Certificate
Given the definition for all x ∈ Σ∗
x ∈ L ⇔ ∃ u ∈ Σ∗ with |u| ≤ p(|x|) and M(x, u) = 1
Lets say the input x = ababab
Then the certificate u shouldn't be longer than p(|x|).
But what would be p(|...
3
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1answer
54 views
How to prove existence of the language
Consider such question:
(Prove or disprove) There exists a language in $TIME(2^{n^2})$ that is not in $NTIME(n)$.
I guess that answer is yes because $TIME(2^{n^2})$ and $NTIME(n)$ are totally ...
0
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1answer
190 views
Are there any estimated, imperfect or fuzzy sorting algorithms?
I'm implementing some estimation metrics that take samples of optimisation functions and estimate their properties. One of the metrics requires the data to be sorted; however, since the metric is only ...
