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!
276
questions
-1
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1answer
79 views
Constructing an NFA for a language defined over $\Sigma = \{0, 1\}$
The language is defined as $$L = \{0^n10^m10^q \mid n,m,q \in \mathbb{N}, q \equiv nm \mod 5\}.$$ Can someone help me get started on this question? I don't know what part of the question I should do ...
-1
votes
2answers
66 views
Why is nondeterminism physically not realizable?
Why it is so hard to make a nondeterministic computer? If such a device is physically realizable then would that be a counterexample to the extended Church-Turing thesis?
0
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0answers
54 views
apply the method of conditional expectations
For a Randomized vertex cover problem
Why there is not much hope of deriving an efficient, deterministic
version using the method of conditional expectation?
I can assume the problem is not ...
0
votes
0answers
21 views
Problem in NP: $EQ1 = \{(p_1,…,p_n): \exists x_1,…,x_m\in Z \ p_1(x_1,…,x_m)=…=p_n(x_1,…,x_m)=0. \}$
I have to following problem to show is in NP class.
$EQ1 = \{(p_1,...,p_n): \exists x_1,...,x_m\in Z \ p_1(x_1,...,x_m)=...=p_n(x_1,...,x_m)=0. \}$
Here $p_1,...,p_n$ are polynomials in m ...
1
vote
1answer
26 views
Non-deterministic Turing machine for $L_1 = \{w\#0^n|w \text{ is a suffix of some $x$ in $L$ with } |x|=n\}$
Show if L is in NP, then also L1 is in NP
$$L_1 = \{w\#0^n|w \text{ is a suffix of some $x$ in $L$ with } |x|=n\}$$
I know that if L is in NP, then there exists a NTM $M_L$ than accepts $x$, ...
1
vote
1answer
42 views
What is $f(n)$ in $NTIME(n)\subseteq DTIME(f(n))$ if $CIRCUITSAT$ is in $P$?
If $CIRCUITSAT$ in $n$ variables and $m$ gates has an $O((nm)^c)$ algorithm for a fixed $c>0$ then $NTIME(n)\subseteq DTIME(O(f(n)))$ for large enough $f(n)$. What is the smallest $f(n)$ in $NTIME(...
0
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0answers
18 views
Proving a problem is NP [duplicate]
I've seen in many textbooks if say we have a problem $Q$, we write a non-deterministic algorithm in polynomial time to solve problem $Q$, and then from that point it results that $Q\in NP$. Why is ...
1
vote
1answer
75 views
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 ...
0
votes
0answers
11 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
votes
1answer
72 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 =...
2
votes
1answer
41 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.
...
0
votes
1answer
180 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
votes
1answer
320 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
votes
1answer
56 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
votes
1answer
158 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
votes
0answers
30 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 ...
0
votes
0answers
56 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
votes
1answer
57 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 ...
1
vote
1answer
71 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(...
6
votes
1answer
53 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
votes
1answer
51 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 ...
0
votes
1answer
43 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 ...
1
vote
2answers
99 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
votes
2answers
42 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?
1
vote
0answers
20 views
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
votes
1answer
49 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 ...
2
votes
1answer
89 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 ...
9
votes
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 ...
4
votes
0answers
87 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
votes
2answers
64 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
votes
1answer
47 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 ...
0
votes
1answer
198 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 ...
1
vote
2answers
153 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 ...
1
vote
0answers
43 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
83 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 ...
5
votes
1answer
112 views
If NP is a subset of DTIME[n^O(log n)] then what happens?
If $\mathsf{NP}\subseteq \mathsf{DTIME}[n^{O(\log n)}]$ then what happens? Does it imply $\mathsf{NP}\neq \mathsf{EXP}$? Is there any other consequences such as $\mathsf{BPP}\neq \mathsf{EXP}$? Does ...
2
votes
2answers
96 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
votes
0answers
84 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 ...
1
vote
1answer
103 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 ...
5
votes
1answer
129 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
votes
1answer
156 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 ...
1
vote
2answers
639 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:
...
1
vote
2answers
85 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 ...
1
vote
1answer
786 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
votes
1answer
59 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
votes
0answers
45 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
votes
2answers
384 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
572 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 ...
1
vote
2answers
781 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,...
4
votes
1answer
187 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 ...
