# 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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7answers
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### Differences and relationships between randomized and nondeterministic algorithms?

What differences and relationships are between randomized algorithms and nondeterministic algorithms? From Wikipedia A randomized algorithm is an algorithm which employs a degree of randomness ...
2answers
8k views

### What is the difference between quantum TM and nondetermistic TM?

I was going through the discussion on the question How to define quantum Turing machines? and I feel that quantum TM and nondetermistic TM are one and the same. The answers to the other question do ...
5answers
13k views

### What is meant by “solvable by non deterministic algorithm in polynomial time” [duplicate]

In many textbooks NP problems are defined as: Set of all decision problems solvable by non deterministic algorithms in polynomial time I couldn't understand the part "solvable by non deterministic ...
3answers
2k views

### What are the conditions for a NFA for its equivalent DFA to be maximal in size?

We know that DFAs are equivalent to NFAs in expressiveness power; there is also a known algorithm for converting NFAs to DFAs (unfortunately I do now know the inventor of that algorithm), which in ...
10answers
8k views

### Why is non-determinism a useful concept?

An automaton is an abstract model of a digital computer. Digital computers are completely deterministic; their state at any time is uniquely predictable from the input and the initial state. When we ...
3answers
5k views

### How to prove that DFAs from NFAs can have exponential number of states?

All non-deterministic finite automata can be turned into equivalent deterministic finite automata. However, a deterministic finite automata only allows a single arrow per symbol pointing from a state. ...
4answers
2k views

### 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 ...
7answers
5k views

### Why NFA is called Non-deterministic?

I have this [kind of funny] question in mind. Why is the non-deterministic finite automaton called non-deterministic while we define the transitions for inputs. Well, even though there are multiple ...
1answer
1k views

### Computational power of deterministic versus nondeterministic min-heap automata

This is a follow-up question of this one. In a previous question about exotic state machines, Alex ten Brink and Raphael addressed the computational capabilities of a peculiar kind of state machine: ...
4answers
688 views

### Push Down Automatons “guess” - what does that mean?

I realize non-deterministic pushdown automata can be an improvement over deterministic ones as they can "choose" among several states and there are some context-free languages which cannot be accepted ...
2answers
990 views

### Classfication of randomized algorithms

From Wikipedia about randomized algorithms One has to distinguish between algorithms that use the random input to reduce the expected running time or memory usage, but always terminate with a ...
3answers
7k views

### Why is NFA minimization a hard problem when DFA minimization is not?

I know that we can minimize DFAs by finding and merging equivalent states, but why can't we do the same with NFAs? I'm not looking for a proof or anything like that--unless a proof is simpler to ...
3answers
3k views

### Is it mandatory to define transitions on every possible alphabet in Deterministic Finite Automata?

Tomorrow is my presentation and I want to clear my conceptsā¦ I've read that in DFA, "For each state, transition on all possible symbols (alphabet) should be defined." Is for each state, defining ...
4answers
6k views

### How does a nondeterministic Turing machine work?

What is differences between deterministic and nondeterministic Turing machines? Different but equivalent models of NDTM. In particular, what is this frequently used phrase "nondeterministically guess"?...
7answers
10k views

### Can we say DFA is more efficient than NFA?

I just started reading about theory of computation. If we compare which is more powerful (in accepting strings), both are same. But what about efficiency ? DFA will be fast compared to NFA, since it ...
3answers
543 views

### Why nondeterminism?

Theory of computation often involves nondeterministic models of computation. Some examples include nondeterministic finite automata (NFAs), nondeterministic pushdown automata (PDAs), and ...
3answers
24k views

1answer
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### Is there a language with non-isomorphic minimum-state UFAs?

For all regular languages L, by the Myhill-Nerode classes, all state-minimal DFAs for L are isomorphic. ā On the other hand, "a regular language may have many non-isomorphic state-minimal nfas". ā ...
1answer
171 views

### 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\...
0answers
219 views

### Why does Non Determinism not enhance FA like it does for PDA

Both Deterministic and Non deterministic Finite Automata can recognize the same universe of regular languages. On the other hand, Deterministic Push Down Automata can only recognize a subset of ...