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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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 ...
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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 ...
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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 ...
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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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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 ...
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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 ...
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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 ...
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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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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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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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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) ...
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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 ...
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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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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 ...
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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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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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103 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 ...
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1answer
110 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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243 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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51 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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422 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 ...
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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, ...
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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....
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317 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 ...
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1answer
211 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
385 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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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 ...
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1answer
43 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 ...
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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 ...
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46 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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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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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(|...
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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 ...
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149 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 ...
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1answer
133 views

Can an algorithm be truly non-deterministic?

I read the term "non-deterministic algorithm" in many places but I don't see how an algorithm can be truly non-deterministic. Typically, there is some source of randomness in these algorithms. If the ...
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1answer
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Understanding trap and dead state in automata

Well, this sounds somewhat basic definitions, but I feel they needs to be clearly defined. In book by Hopcroft et. al., there is an excerpt: ...a dead state, that is, a nonaccepting state that ...
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596 views

Number of states in NFA and DFA accepting strings from length 0 to n with alphabet Σ= {0,1}

The question is in title. Let me repeat: What are the number of states in NFA and DFA accepting strings from length 0 to n with alphabet $\Sigma = {0,1}$ I feel both NFA and DFA will take ...
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1answer
63 views

Is this language NP Hard?

$L=\{$$($$m$,$w$,$n$$)$| $m$ is an encoding of a non-deterministic Turing machine, $w$ is any word/string in the closure of alphabet, i.e. $w\in\Sigma^*$, $n$ is any positive integer, i.e. $n\in\Bbb{Z}...
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Where is proof that palindrom language is nondeterministic? [duplicate]

It is well-known that the language over $T$ with at least 2 symbols is nondeterministic. for simplicity, the language $\{ww^R: w\in\{a,b\}\}$ (even-length palindroms of $a$, $b$) is context-free, but ...
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Do NFAs with $\varepsilon$-moves never terminate?

Suppose in an NFA we have an $\varepsilon$-move from a state $q_0$ to $q_1$. According to Sipser, Without reading any input, the machine splits into multiple copies one following each of the ...
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Questions on Sipser's NP implying verifiability?

I've revisited trying to understand the proof to why NTM exists iff there is a verifier. I think I'm finally understanding the proof but I want to make sure and thus have some questions as follow up ...
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NFA accepting $L=\{wbbav \;|\; w \in \{a,b\}^*, v \in \{a,b\}^+, v\; has\; suffix\; a\}$

I have to construct NFA that accepts language $L=\{wbbav \;|\; w \in \{a,b\}^*, v \in \{a,b\}^+, v\; has\; suffix\; a\}$. My solution is this automata: Can you tell me, if this is correct or not? If ...
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405 views

Is every decidable language a deterministic context free language?

I'm trying to get a better understanding for the relationship between decidability and a few other things so that I can get a better grasp of the topic. Any info helps! Is every decidable language a ...
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Is there a method to compress all data without loss (lossless compression)?

I know that the answer is no but I'm not sure why. Here's where I started. We know that all data with length $n$ Bits and minimum $1$ Bit can be compressed, either lossless or lossy. But how do I ...
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show doubly connected graph is NL complete

The question:A directed graph is doubly connected if every two vertices are connected by a directed path in each direction. Let DCG = {| G is a doubly connected graph} Prove that DCG is NL-complete. (...
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Implications of $NL=P$

What would be some implications of $NL$$=P$? Would it be possible to get recommendations on good sources/papers I can read to learn more about this? Thank you
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96 views

Prove: if $\delta_D(q0, w) = p$ then $\delta_N(q0, w) = {p}$

In my textbook, it presents the theorem, "A language L is accepted by some DFA if and only if l is accepted by some NFA". My textbook explains that the "if" portion of the proof is given by the subset ...
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254 views

Minimal DFA with more states than its equivalent NFA

I understand that using a bad case for subset construction as provided through an example in the book - Introduction to Automata Theory, Languages and Computation, we can definitely have an NFA with $...
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124 views

Complement of Mealy machine

How could one reasonably define and construct the complement of a deterministic Mealy machine? My intuition is that the complement should give exactly the opposite of output strings after a specific ...