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!
297
questions
0
votes
0answers
63 views
Generalization of automaton - Sipser example 1.33
I am trying to construct a nfa that generalizes Example 1.33 found in the book Introduction to the Theory of Computation by Sipser, but I am quite sure
that my transition function is wrong. I'd like ...
1
vote
2answers
32 views
How are useless states created NFA to DFA
So I understand how to convert an NFA to a DFA, however my question is, on a conceptual level, how and why are useless states created, and how can you (if there is a way) convert an NFA to a DFA ...
4
votes
1answer
157 views
Show $L = $ { w $\in (a,b) ^* $| for every u substring of w, $-5\le|u|_a−|u|_b\le5\}$ is regular
I try to show that this language is regular:
$L = $ { w $\in \ (a,b) ^ * $| for every u substring of w, $-5\le|u|_a−|u|_b\le5\}$
If I build a NFA and run on it every substring of w (skip other letters ...
0
votes
1answer
99 views
Is it incorrect too say that this function problem cannot be in $FNP$?
Decision Problem:
Is $2^k$ + $M$ NOT a prime?
$K$ and $M$ are our inputs represented as integers.
Function Variant: Output the result of $2^k$ + $m$
We can consider, $M$ = $0$.
Proof that calculating ...
-1
votes
1answer
25 views
Formal definition of non deterministic PDA
How would you convert the following formal definition of deterministic pushdown automata into non deterministic ?
Deterministic PDAs In general terms, a deterministic PDA is one in
which there is at ...
0
votes
0answers
13 views
Nondeterministic Turing Machine for $L^*$
If $T$ is a Turing Machine that accept a language $L$, I want to define a Turing Machine $T'$ such that accepts the language $L^*$.
An approach:
$T'$ is a nondeterministic Turing Machine which has ...
1
vote
1answer
38 views
Is this push-down automaton non-deterministic, as JFLAP states?
There is a tool called JFLAP, which, among other things, can analyze push-down automata, and find non-determinism.
In this example it is detecting non-determinism in state ...
0
votes
1answer
25 views
Can an $NDTM$ simultaneously perform a set of operations on all strings of a given length?
Can an $NDTM$ perform a set of operations on all strings of a given length $b$, at the same time? Aka can it operate on all strings of a given length by doing something like: spawn $2^b$ branches then ...
2
votes
1answer
35 views
Is s-grammar powerful enough to generate all possible DCFL?
In s-grammar all productions are in form of A → 𝑎𝛼 , A∈V , a∈T , 𝛼∈V*
"... and any pair (A, a) occurs at most once in P." [P. Linz, 6th ed. , p. 144]
s-...
0
votes
2answers
129 views
Can a non-deterministic machine merge its branches?
Does an NDTM have the power to combine computational branches ie. can a result from branch A be used in the next step in the computation along branch B? Can branches use each others' results, ...
-1
votes
1answer
29 views
Can enumeration take advantage of non-determinism?
If I want to build an NDTM to enumerate a list (of all Turing machines, for example) is there a way to use non-determinism to "speed this up" or take advantage of it somehow?
What types of of r.e. ...
1
vote
1answer
14 views
Is $NSPACE(S(n)) \subseteq DSPACE(S(n))$ if $S(n)$ is time-constructible?
I read from Savitch's theorem that given a fully space-constructible function $S(n)$, we have
$$
NSPACE(S(n)) \subseteq DSPACE(S(n)^2)
$$
Am wondering, what happens if $S(n)$ is fully time-...
0
votes
1answer
35 views
How is the NP verifier polynomial?
If we start with the definition of L being in NP if "there exists a polynomial NTM that decides L" (where polynomial for an NTM means the length of the worst run as a function of the size/length of ...
2
votes
1answer
64 views
When our two-state PDA constructed from CFG is non-deterministic PDA?
We can always convert our GNF-CFG/CNF-CFG to a two-state PDA but i'm wondering when our PDA is non-deterministic? i'm sure we can not make DPDA for non-Deterministic-CFL , and i suspect that same rule ...
2
votes
1answer
21 views
State complexity of converting epsilon-NFAs to NFAs without epsilon transitions
I am well-aware of the result showing that one can convert an epsilon-NFA (that is, an NFA with epsilon transitions) $A$ to an NFA without epsilon transitions $A'$, where $L(A) = L(A')$.
Is there a ...
1
vote
1answer
54 views
If anything can be verified efficiently, must it be solvable efficiently on a Non-Deterministic machine?
Suppose, I wanted to verify the solution to $2$^$3$. Which is $8$.
The $powers~of~2$ have only one 1-bit at the start of the binary-string.
Verify Solution Efficently
...
1
vote
0answers
81 views
Question about proof of Lemma 2.41 - Sipser book
Doesn't the modification described in paragraph three potentially introduce non-determinism? For example, say neither a, b, x, nor y is the empty string (denoted e). If in the original machine P we ...
1
vote
2answers
95 views
Conversion of nfa with self-loop to one without self-loop
For every nondeterministic finite state automata that has self-loop(s), there exists an equivalent nfa that does not have any self-loop. How can we prove this statement in a general basis without the ...
0
votes
1answer
33 views
Non Deterministic Turing Machine
Can anyone give an example of a NDTM for a problem (which cannot be solved with DTM) with transition function?
0
votes
2answers
81 views
In a NPDA if the stack is empty, where the start/end state are the same can you go again
Thoughts
I am wondering if you get a string that goes through the NPDA and arrives back at q0 can I go through the NPDA again so that the last number in the string is not fixed, or is it that once I ...
3
votes
1answer
122 views
Arden's Rule, DFA & NFA to regular expressions
I have been trying to figure out the Arden's Rule and the equational method to transform DFA's & NFA's to RE. I know what the rule state:
if x = s + xr
then x = sr*, with $s,r\in$ Regular ...
1
vote
1answer
45 views
Is $L \subset 1NL$ when $L \neq NL$? [closed]
A log-space Turing machine has a read-only input tape, a write-only output tape and uses at most $O(\log n)$ space in its read-write work tapes. The classes $L$ and $NL$ contain those languages which ...
-1
votes
1answer
94 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
81 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
votes
0answers
55 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 variables ...
1
vote
1answer
37 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
57 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
votes
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 ...
2
votes
1answer
221 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
16 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
80 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
64 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
371 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
357 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 $f(...
5
votes
2answers
136 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 ...
1
vote
3answers
438 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 ...
3
votes
0answers
48 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
72 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
77 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
328 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
56 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
62 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
55 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
143 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
59 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
31 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
71 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 ...
3
votes
1answer
114 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 ...
