Talk:Nondeterministic algorithm

In the intro, "a nondeterministic algorithm is an algorithm with one or more choice points where multiple different continuations are possible". What's a choice point? What's a continuation?

I don't know how to address this comment. If anyone else feels it should be clarified, please do. Rp 16:06, 20 October 2007 (UTC)

In need of massive work

Wow, there's about 1.2 zillion different types of nondeterministic algorithms (if you include things like stochastic methods, etc). This article is in need of serious attention. Perhaps I'll have to see to that! - 172.133.246.35 06:42, 2 December 2006 (UTC) (JustinWick)

I think it's better to discuss stochastic methods separately, and link to them here. Rp —Preceding comment was added at 16:02, 20 October 2007 (UTC)

Is "nondeterministic algorithm" and "probabilistic deterministic algorithm" the same?

In the example "Primality testing" the "Guess an integer..." part of a concrete program/implementation can only use a random number generator to get the job done. Does this mean, that "nondeterministic" and "probabilistic deterministic" are the same in this instance?

It is not the same thing. A probabilistic algorithm is an algorithm in which nondeterminism is resolved by the use of probability. You don't just say that multiple choices are possible, you also give the likelihood for each of the choices to be made. Rp 18:54, 19 October 2007 (UTC)

I removed another sentence from that example which maintained the suggestion that nondeterminism and random choice are the same. Rp (talk) 20:15, 30 March 2009 (UTC)

Merge

Can anyone explain why the merge with nondeterminstic programming is a good idea? Or OK if I just remove the merge tags? Sam Staton 16:20, 8 October 2007 (UTC)

The term "nondeterministic programming" feels like a contradiction to me. We don't usually combine these two words, even though it makes sense to do so. Rp 18:55, 19 October 2007 (UTC)

I have also read the article. It's too sketchy but it does seem to have merit, as far as I can tell (I am not familiar with the systems mentioned). I think merging it here would be a bad move, because this article is about the idea of a nondeterministic algorithm, which is separate from the idea of actually programming systems in terms of them. Rp 15:59, 20 October 2007 (UTC)

Reverted edit

I reverted an edit by an anonymous editor. The sentence "A nondeterministic algorithm as an algorithm that, given the same input, may produce different results." is not true: the important thing about a non-deterministic algorithm is that it may make (nondeterministic) choices during execution. Also the first paragraph, even as it stands, is certainly not a "formal definition". If this is unclear, I'm happy to discuss. Sam Staton 10:06, 17 October 2007 (UTC)

I don't see how the edit being made by an anonymous editor is relevant. That being said, the point of the summery of any article is to make the subject matter approachable.

The 'old summary' is too technical and most definitely not approachable. Considering the old summary to be 99% accurate and completely unapproachable, and considering the new summary to be 80% accurate and totally approachable, I believe the less accurate and approachable definition is the better choice. Wikipedia guidelines also dictate that summaries should be approachable even if they are slightly inaccurate. Users wanting to know more about the subject will continue reading and learn the more correct definition, and people uninterested will leave knowing, for the most part, what they came to learn. If we turn these readers off from reading the article by slapping them across the face with an overly complicated summary, the reader loses and the writer doesn't gain anything.

Your concern about the 'new summary' being inaccurately is unwarranted anyway. Picking apart the word , the inverse of deterministic, yields no importance to making choices. If something is determined then the output has already been decided even before completion. The inverse would be: If something is not determined then the output has not already been decided. There is no implication of choices being made, and if there were and you still think its extremely important, than add that to the simple summary.

I have brought back the simple summary and have fixed a typo in it. I have also renamed the 'formal' definition to 'explicit' definition per your suggestion, which I agree with.

Hello, I think you misunderstood my comment - I don't hold anything against anonymous editors, and I respect your right to anonymity. I just wanted to identify the edit I was talking about.

As I said, it is quite reasonable to ask for a simpler first sentence. But I maintain that your first sentence was far too simple, to the extent that it was wrong. A great many important nondeterminstic algorithms do not return different results for a fixed input. These kinds of algorithms are really important in the study of nondeterminstic polynomial time, in complexity theory. This is one of the main fields of computer science where nondeterminstic algorithms are important. I'm not sure how familiar you are with this.

In line with this, I have tried to correct and improve the opening first sentence. I hope its clearer than the longer paragraph, without being misleading. It's still not perfect, I admit. (In case you find I don't reply to any further discussion: I'll be away now for a few days.) I also changed 'explicit' to 'detailed', since I think that is more appropriate. All the best, Sam Staton 08:42, 18 October 2007 (UTC)

I do not feel it is appropriate to include the word 'deterministic' in the summary of this article because it goes along the lines of using a a word to describe it self. Again, I stress that explicitly stating that choices are being made isn't necessary. I believe that the word algorithm implies a decision making process is occurring in some fashion.

I don't know whether I understand your objection, and I have no idea how to address it. Can you please suggest a rewording that would be more to your taste? (And sign your comments by appending four tildes.) Thanks. Rp 15:52, 21 October 2007 (UTC)

examples

Examples 2-4 leave a reader with no clue why they describe nondeterministic algorithms, each for its own reason I don't even want to start explaining. Is there an expert in the subject who can do a decent job here?

I don't think of merge sort as a nondeterministic algorithm at all. Example #4 is an algorithm, but not for the problem described. I'm a logician though, not a computer scientist, and they are known to be sufficiently bad with they terminology that I am reluctant to edit too much without having reference to a CS text, which I don't. — Carl (CBM · talk) 23:59, 26 April 2010 (UTC)

I think all the examples on the page are terrible. Can we just delete all of them? None of them seem to exhibit nondeterminism in the sense of nondeterministic Turing machines or a nondeterministic finite-state machine. --Robin (talk) 02:52, 27 April 2010 (UTC)

I agree with that. My only concern is that maybe the term "nondeterministic algorithm" is used more generally in CS, not just referring to automata. — Carl (CBM · talk) 11:07, 27 April 2010 (UTC)

I checked the incoming links to the page, and it looks like there are two different meanings of the words "non-determinism" that both link to this page. The first is in the sense of non-deterministic TMs, and the second meaning seems to be anything that is not deterministic (which could mean a random choice, or a choice where the user is not told how the choice is made). This page should probably then reflect these two meanings, or have one of them redirect to a different page. --Robin (talk) 13:06, 27 April 2010 (UTC)

If you want to write an article about nondeterministic automata, call it Nondeterministic automaton. If you think the examples are wrong, improve them or at least explain what's wrong so it can be fixed by others. Rp (talk) 08:42, 4 May 2010 (UTC)

I can tell you what I think is wrong: I have never heard the word "nondeterministic algorithm" used to specify an algorithm that is simply underdefined, as in the merge sort example on this article. As far as I can tell, with the way this article uses its terminology, "put the elements in order" is an example of a nondeterministic sort algorithm. Compare the "shopping list" example. It's hard for me to call these "algorithms" in any sense. — Carl (CBM · talk) 11:32, 4 May 2010 (UTC)

I think you have a point - the term isn't commonly used in such a wide sense. But I can't see how to make a good definition that would exclude such examples. Rp (talk) 07:58, 8 June 2010 (UTC)

Nondeterministic doesn't mean an algorithm that makes choices

There are many algorithms that may make an arbitrary choice at some point that are not considered nondeterministic by any source I'm aware of. In nearly any search, there is a choice of which node to visit next, but that does not make the search nondeterministic. In quicksort, any element may be chosen as the partition, but that does not make quicksort nondeterministic. According to CLRS, a multithreaded algorithm is nondeterministic if its behavior might vary from run to run. That is, the algorithm makes a choice, and on different runs that choice may differ. In other words, the exact behavior of the algorithm cannot be determined ahead of time. I will rework this article entirely unless someone can come up with a source that contains a different definition. -- Schapel (talk) 17:08, 16 August 2011 (UTC)

• I am not sure if you reworked it but this presentation seems completely wrong. Two of the references get it right with one reference claiming: (A nondeterministic algorithm is) " A conceptual algorithm with more than one allowed step at certain times and which always takes the right or best step. It is not random, as in randomized algorithm, or indeterminate. Rather it has the supercomputational characteristic of choosing the optimal behavior."

• Can we please copy that definition. Nondeterministic algorithms don't really have physical counterparts as in algorithms with choice points which choose a progression. Rather, they are used in studies of conceptual algorithms and formal verification. I.e., they are convenient in providing specifications. A (deterministic) sorting algorithm is equivalent to its nondeterministically specified algorithm which simply chooses the right ordered sequence. Typically, a nondeterministic algorithm doesn't have a direct computational interpretation which seems to be the source of all the confusion here. Providing a definition as if it has a computational interpretation completely misses the point.

• The introduction is not 80% correct, it is 100% wrong. This article needs a rewrite. 86.82.44.193 (talk) 14:01, 5 July 2015 (UTC)

• This is how it was explained in the formal languages course I took as a student: a nondeterministic algorithm is not an algorithm that makes choices, but one that leaves choices open. It has at least one explicit choice point for which the decision which of the available options to take is left open, i.e. not made by the algorithm, and while running, any of the available options may be taken. It is not the case that the algorithm always magically decides on an optimal choice. Now a string is said to be accepted by a nondeterministic algorithm or device if there is at least one possible run, i.e. at least one particular set of choices for every choice point encountered during runs, such that the final result is to accept the string. As it was explained to me, this is not a property of nondeterministic algorithms as such, but only of how they are applied in defining nondeterministic acceptance of languages. So quicksort in which some choice point, e.g. the choice of how to partition, is left open in this way, is indeed a nondeterministic algorithm. I do agree that it is confusing to mention a sorting algorithm as an example, because the relationship between such an algorithm and its intended results (a sorted input string) is completely different from the relationship between a nondeterministic string accepting algorithm and its intended result (acceptance or nonacceptance of the input string). Rp (talk) 21:10, 6 July 2015 (UTC)

• I don't think the above descriptions are improvements. Calling the options at a choice point "steps" is confusing to me because it suggests to me that they are made in sequence instead of being alternatives. Saying that "on different runs the choices made may differ" is correct but not strong enough: it is essential that whenever a choice is left open, any of the available options can be taken during a run. Saying that a deterministic sorting algorithm "simply chooses the right sorting sequence" or that a nondeterministic algorithm doesn't have a direct computational algorithm doesn't make sense to me. Providing a definition as if it has no computational interpretation would completely miss the point! It would suggest that nondeterministic algorithms somehow can't be executed by machines, when the whole point is that they can be. Rp (talk) 21:10, 6 July 2015 (UTC)

• I disagree with how it was presented to you during your studies. "Now a string is said to be accepted by a nondeterministic algorithm or device if there is at least one possible run, i.e. at least one particular set of choices for every choice point encountered during runs, such that the final result is to accept the string." This is (near) correct. A nondeterministic machine accepts a string if it accepts it along one of its execution paths. I find you still give it too much of a computational characteristic in your other treatment.

• Your example regarding sorting doesn't express the 'power' of nondeterministic algorithms as the nondeterministic quicksort algorithm just leaves open a 'probabilistic' choice. I can give a nondeterministic algorithm which will nondeterministically choose a sequence and check all original elements occur and are sorted. That shows the fundamental difference between nondeterminism and determinism whereas your example does not.

• I think I said there is no 'direct' executionable interpretation for nondeterministic algorithms. I agree it's easy to miss the emphasis on 'direct'. Of course there are, if you accept possible exponential blowup. Which is another problem with your example, it doesn't provide insight in why nondeterministic algorithms can only be 'exponentially' simulated (P=NP?). Your example insists on the view that nondeterministic algorithms are a simple variant of deterministic programming with choices left open which can be simulated by choosing _any_ execution path whereas it is about _all_ execution paths.

• I agree that formally nondeterministic algorithms don't leave choices open. But the definition given on the other site is an 80% correct explanation whereas the introduction, I remain, now still is 100% wrong.86.82.44.193 (talk) 13:57, 7 July 2015 (UTC)

You got the meaning of "nondeterministic algorithm" completely wrong

In the modern theory of algorithms and complexity theory the term "nondeterministic algorithm" has a very specific meaning. Nondeterministic algorithm are not opposite of deterministic one -- although the way English language works suggests so. Nondeterministic algorithm is nondeterministic in the same way as Non-deterministic_Turing_machine is, and it doesn't make any sense to speak here about "execution" or "state" of such algorithm. Because you don't execute nondeterministic Turing machines in the way you execute Python programs.

A nondeterministic TM can accept or reject an input -- the input is accepted if and only if there is a sequence of nondeterministic choices which can lead to the ACCEPT state of TM. And this definition of nondeterministic TM agrees with the way nondeterministic finite automatons, branching programs, decision trees or circuit are defined. All these different models of computation have deterministic, nondeterministic and probabilistic analogs -- and all of these are examples of nondeterministic algorithms.

You can read more about this for example Arora and Barak's complexity textbook -- http://theory.cs.princeton.edu/complexity/. To summarize, an algorithm can be of these mutually exclusive types:

* Deterministic
* Nondeterministic
* Probabilistic
* …

So nondeterministic algorithms do not include probabilistic ones.

I think the best thing to do with this article is to either just replace it with redirection to the article Non-deterministic_Turing_machine, or to define here what is nondeterminism the way it is done by Arora and Barak, and give further links to articles about nondeterministic TMs, FAs, circuits and so on.

Maybe there are some other fields of CS of which I'm not aware of, and they have their own definition of nondeterminism. In this case this article probably should mention that too, but focus more on the Arora&Barak's definition of nondeterminism -- because this is what they call nondeterminism at any university course on algorithms today. — Preceding unsigned comment added by Ph14nix (talk • contribs) 14:33, 22 October 2019 (UTC)

I agree that the article is confusing. In fact, its subject is not "nondeterministic algorithm" but "nondeterministic computation". I have added a hatnote for clarifying the subject of the article, and redirecting to Nondeterministic model of computation. However, there was no article of this name, so I have created it as a redirect to Non-deterministic Turing machine. Also, I will request a move of Nondeterministic algorithm to Nondeterministic computation, which was a redirect to Non-deterministic Turing machine (I have just changed the target into Nondeterministic algorithm).

IMO, Nondeterministic model of computation should be expanded into a true article, at least a WP:stub. Are you willing for that? D.Lazard (talk) 17:20, 22 October 2019 (UTC)

Requested move 22 October 2019

Nondeterministic algorithm → Nondeterministic computation – The present title is clearly ambiguous as shown in the preceding thread of this talk page, and the disambiguation hatnote that I have added to the article. The proposed title is much clearer as referring to effective computation (the subject of the article rather than to abstract algorithms. D.Lazard (talk) 17:36, 22 October 2019 (UTC)

• Oppose This article is, in its current state, confusing, but the proposed rename won't resolve the confusion. It seems there are at least two kinds of things that are referred to as "Nondeterministic algorithms" in the literature: A) Algorithms written using primitives associated with nondeterministic models of computation/NTMs. This is discussed above by Sam Staton, RobinK, and Ph14nix above, and in this EL (and the NIST EL and the Floyd paper) B) Algorithms whose behaviour might vary from run to run. According to Schapel above, CLRS uses this sense (though they don't indicate whether the work specifically uses the phrase "nondeterministic algorithm"). This other meaning is also alluded to in some other comments above, including a reply from Robink. Right now, this article gives a mish-mash of concepts A and B, which is bad, because they're totally different.

Most of the article's current content, and all its references/external links (except CLRS), relate to meaning A. We also have pretty good evidence that the current title is the WP:COMMONNAME for meaning A. The remnants of B should therefore probably be swept away (possibly into a separate article, if there's enough coverage of it as a distinct concept. Colin M (talk) 00:19, 24 October 2019 (UTC)