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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Deterministic vs. Non-Deterministic PDA?

The following is an example of language $a^nb^n$ where $n \geq 1$ From what I have heard that in finite state machines if you see epsilon moves, then it is NFA otherwise it is DFA. But in this case, ...
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1answer
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How convert instances of a language efficiently into 3SAT instances?

The following question is from Sanjeev Arora and Boaz Barak ( not homework ) Show that for every time constructible $T:N \to N$, if $L \in NTIME(T(n))$ then we can give a polynomial-time Karp ...
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1answer
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Why is my trivial reasoning for $PSPACE = PH$ wrong?

If $\sum_i^p$ denotes $ith$ polynomial hierarchy. And $\sum_i TIME( T(n) )$ denotes set of languages accepted by $T(n)$ time alternating Turing machine $M$ whose initial state is labeled $\exists$ and ...
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NSPACE for checking if two graphs are isomorphic

I was studying nondeterministic Turing Machines and came across the following question: Describe a nondeterministic Turing Machine (NTM) that only accepts two graphs (G1 and G2) if they are ...
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How do cycles of non-consuming transitions in NFAs influence their halting properties?

I am in a class that is going over NFAs. The way they are described is a set of states, one of which is the start state, zero or more are accept states, and one or more transitions between them, which ...
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How can I show that the Cook-Levin theorem does not relativize?

The following is an exercise which I am stuck at ( source: Sanjeev Arora and Boaz Barak; its not homework ) : Show that there is an oracle $A$ and a language $L \in NP^A$ such that $L$ is not ...
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1answer
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Why is simulation by non deterministic Turing machine faster than a deterministic one?

A deterministic universal Turing machine $U_D$ can simulate a deterministic turing machine $M_D$ in $O(T(n)log(T(n)))$ where $M_D$ runs in $O(T(n))$. But I came across an exercise in Sanjeev Arora and ...
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679 views

NL and NP compute different binary relations, so what?

Let the binary relation computed by a nondeterministic transducer be the relation between input strings and the possible output strings the transducer can produce (and accept) for the given input ...
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1answer
122 views

How Can I Recognize When to Use ε-Transitions in an NFA?

I am learning about finite automata for the first time. I am having trouble understanding the purpose of ε-transitions in an NFA, which seem to be crucial to counting the number of states in an NFA ...
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2answers
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How does the NFA decide in a state where there are multiple equally valid “next states”?

How does the NFA decide in a state where there are multiple equally valid "next states"? Such as here: How does it decide on which state it takes to with 1?
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How do I verify that a DFA is equivalent to a NFA?

I'm learning how to convert NFAs to DFAs and I want to make sure I'm doing it right. Obviously, going back in the other direction isn't a thing. Does anyone know of an algorithm to check that a DFA is ...
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1answer
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What input does this NFA accept?

I'm trying to find out what strings this NFA would accept. From what I understand, an empty string would work, as well as any string that has nothing but 0's. But for strings containing 1's, I'm a ...
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1answer
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Finding an automaton with a given number of states

Define an NFA with 4 states that is equivalant to the following Regular Expression. $(01 + 011 + 0111)^*$. My main problem is that to check for a string of length 4 (...
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2answers
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Can a deterministic language be accepted by a deterministic Push Down Automaton?

I have a question that asks me to show that the PDA of the language L is not deterministic, but that the language is nevertheless deterministic. I was under the assumption that any deterministic ...
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1answer
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How to remember NFA's choice on a certain computation?

I'm working on solving the question answered at this page but with different values at the table, my alphabet is {a,b,c} Words that have the same right- and left-associative product Currently I'm in ...
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0answers
103 views

Dangling else determinism

The natural grammar for dangling "else" is ambiguous. But there exists an unambiguous version of the grammar that links the "else" to last uncompleted "if" statement. Is this version also ...
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2answers
381 views

If the universe were predetermined, would non-deterministic automata still make sense?

If the universe were governed by predeterminism (i.e. some deity decided in advance how everything, ever, would play out), would the notion of non-deterministic automata make sense? Or would it not, ...
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1answer
595 views

What language should this NFA recognise?

I am trying to figure out which language does the following NFA (taken from a Sipser's book "Introduction to theory of computation") recognise From my understanding, this NFA accepts strings that ...
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1answer
576 views

Can we show that non-determinism adds no power, for some specific running time?

$NP = \cup_{k \in \mathbb{N}} NTIME(n^k)$ $P = \cup_{k \in \mathbb{N}} TIME(n^k)$ Can we show that $NTIME(n^k) = TIME(n^k)$ for a specific $k$? For how large of a $k$ can we show the above ...
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1answer
607 views

What real-world computer languages cannot be described by deterministic grammars?

Are there any examples of real-world computer languages that are non-deterministic? By computer languages I include programming languages, markup languages, query languages, modeling language, ...
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1answer
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Non-deterministic algorithms and Tautologies

I am studying the lecture The Complexity of Propositional Proofs. ​Here there is a definition together with a discussion (page 3). I don't understand that discussion. Let $F$ denote the set of ...
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How to construct an NFA [duplicate]

I am trying to learn how to construct an NFA state diagram. $$M = \{q0, q1, q2\}, \{a,b\}, \delta, q0 , \{q2\}$$ $δ(q0,a) = q0; \delta(q0,b) = {q0,q1}; \delta(q1,a)= {q0, q2}; \delta(q1,b) = {q1}; \...
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1answer
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Is non-determinism in a non-deterministic turing machine different from that of finite automata and push down automata?

Let a input string be given as $w_1w_2...w_n$. Then if a NFA is currently in state $r$ ( and has read the input upto alphabet $w_i$ ) then before reading the next input symbol the NFA splits into two ...
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Language of strings of lengths that are prime is regular? Is C^* regular? [duplicate]

With $\Sigma = \{a\}$ I want to see if a language $C = \{a^p \ | \ p \ \text{is prime}\}$ is regular and whether or not $C^*$ is regular. How would I go about showing whether $C$ or $C^*$ are regular?...
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1answer
177 views

When does a PDA split?

In case of NFA, if the NFA is in a state and reads $\epsilon$ ( empty string ) the NFA splits in to two, with one being at the current state and other with the state along the $\epsilon$ transition. ...
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2answers
236 views

Use DFA minimization on LR(1) states

I have recently started reading more about context-free parsing techniques, in particular LR parsing. As I have read, LR state transition graph (or table(s)) used for finding handles in sentential ...
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392 views

NFA that accepts binary strings starting with 1 and with at least 01, or at least 010, or both

Im not sure if I am understanding this question correctly. Its a problem without a solution in my text. Starting with 1, and at least 01 or at least 010 or both these substrings..... So a regular ...
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1answer
117 views

Executing an NFA

I am trying to verify that the NFA below does not accept babba. However, when I tried to do it by hand I must have made a mistake: $$\{q_1\}, \{q_2,q_3\}, \{q_1, ...
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4answers
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Defining the halting problem for non-deterministic automata

The primary definition of Turing machine (TM), at least in my own reference textbook (Hopcroft+Ullman 1979) is deterministic. Hence my own understanding of the halting problem is primarily for ...
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3answers
399 views

Are deterministic and nondeterministic Cellular Automata equivalent?

It seems that in CA context nondeterministic (ND) means probabilistic, not ND as in NFSMs. At least I haven't seen a paper or book which discusses NCAs, without talking about probabilistic CAs. I ...
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Smallest class of automata model whose corresponding language class contains CFL and is closed against (dis)allowing nondeterminism in the model

From a comment, an interesting question popped up. The class of CFLs (the languages recognized by PDAs) are obviously not closed under nondeterminism - what I mean by this is that deterministic PDAs ...
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1answer
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Converting this NFA to Turing Machine

I'm asked to choose a DFA and convert it to NFA and then convert it to Turing machine... I have done the first two parts as follows: DFA: --> NFA: --> Turing machine: ??? I haven't found any ...
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784 views

extended transition function for NFAs

Below I am using a DFA transition function that is extended to accept words instead of just symbols. Let's say it is given that the following information is true: $$\delta(q_0, 0^3) = \delta(q_0, 0^6)...
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0answers
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Formal language properties and finite state machines [closed]

What are properties of a formal language? Which and how would they be needed to prove that some Non-Deterministic finite state machine can accept a given language?
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1answer
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NDTM for Graph Clique Problem in poly-time

I am having a doubt. This is my NDTM algorithm: GCP(G, k): generate a list with k distinct nodes from graph G generate an adjacency matrix, fill it with 1 if an edge exist, 0 otherwise check if ...
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3answers
2k views

Why doesn't parallelism necessarily imply non-determinism?

I'm a student reading a book on threads. And I got when I got to non-deterministic and parallel programs, I got a bit confused. I hope you can help me out. I understand the difference between ...
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1answer
94 views

How can I quickly guess if L is context-free or det. context-free?

I have a language, for example $\{a^m b^n c^n \mid m, n \in \mathbb{N}, m = 2n\}$ $\{a^l b^m \mid l, m \in \mathbb{N}, l=4^m\}$ How can I see at a glance whether the language is deterministic ...
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1answer
283 views

Language described by inverting accepting states of NFA

Connecting to When states that are not accepting states become accepting states in NFA, what happens?, what is the formal language described by inverting accepting states of NFA? By inverting, I mean ...
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4answers
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What is determinism in computer science?

I was asked if my computer program (in Java) was deterministic. I'm wondering how could it be not? There is no such thing as a non-deterministic Java program right? Even if I use a random number ...
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2answers
484 views

Can we build a nondeterministic decider PDA using two PDAs accepting a language and its complement?

When talking about turing machines, it can be easily shown that starting from two machines accepting $L$ and its complement $L^c$, one can build a machine which can fully decide if a word is inside $L$...
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How does an NFA use epsilon transitions?

In the picture below, I'm trying to figure out what exactly this NFA is accepting. What's confusing me is the $\epsilon$ jump at $q_0$. If a $0$ is entered, does the system move to both $q_0$ and $...
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1answer
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Is there $L$ such that $L$ and $\bar L$ are context free, but $L$ is not deterministic context free?

The usual candidates for context free languages whose complement is also context free, but they are not regular are the Deterministic Context Free Languages ($DCFL$). For example, $L=\{a^nb^n\mid n\...
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1answer
377 views

Why is it that the transition function for DPDA's only works for 1 alphabet symbol, and 1 stack symbol?

Why is it that the transition function for DPDA's only works for 1 alphabet symbol, and 1 stack symbol? Say f is the transition function, why does having ...
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1answer
75 views

Space penalties for the simulation of a non-deterministic Turing machine by a single-tape deterministic Turing machine

If I have some non-deterministic Turing machine $NDTM$ running some process $Q$ and I wish to simulate the same process $Q$ with a deterministic single-tape Turing machine $DTM$, there will of course ...
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1answer
205 views

Non-deterministic algorithm to check if a list has some given value

I know that I can build a non-deterministic algorithm with a CHOICE function that verifies if a value x is in an array in O(1) ...
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2answers
284 views

Using SMT solvers to generate random solutions to given predicate

I am interested in generating random solutions to predicates. I only need SMT for integers with the following predicates/functions <, >, <=, >=, ==, !=, +, * The algorithm I want should produce ...
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1answer
187 views

The communication complexity of non-equality

I'm familiar with the fooling set technique to obtain lower bounds for communication complexity protocols. The most basic example is the equality function for which the diagonal matrix gives the ...
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1answer
5k views

NFA - string acceptance (decision problem) test

I am interested in testing for a given string (w) whether it is in the language (L) defined by a nondeterministic finite automaton (A). I have some blurry point in my mind. What is the complexity of ...
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2answers
705 views

Are nondeterministic algorithm and randomized algorithms algorithms on a deterministic Turing machine?

An algorithm on an abstract machine is a finite sequence of operations of the machine. (Correct me if I am not correct.) However, there are different kind of algorithms, such as deterministic, non-...
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Are DCFLs closed under reversal?

According to this chart, DCFLs are closed under reversal. However, I am not convinced as the intuitive proof (reversing the arrows of the controlling finite state machine and switching the pushes and ...

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