# 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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### 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 ...
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### 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 ...
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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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-...
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### 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, ...
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### 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. ...
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### 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-...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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?
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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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?
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### 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 ...
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### 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 ...
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### 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 $x$, ...
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### 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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### 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 ...