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1answer
45 views

What is the name of the word problem for free groups under straight line program encoding?

I believe that the word problem is the problem to decide whether two different expressions denote the same element of a suitably defined algebraic structure. For simplicity, let us focus on free ...
0
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1answer
13 views

Can you form a group with assembly instructions under the MIPS-32 architecture?

Would it be possible to form such a group using the ADD instruction and the NOT instruction?
5
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1answer
52 views

What can be said in general about a homomorphism between two regular languages?

In other words: is a homomorphism always guaranteed to exist between two arbitrary regular languages? If not (which I suspect), are there only a finite number of classes of languages, for which we can ...
1
vote
1answer
138 views

Algorithm: Cracking the Safe

A safe is protected by a four-digit $(0-9)$ combination. The safe only considers the last four digits entered when deciding whether an input matches the passcode. For instance, if I enter the stream ...
0
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1answer
42 views

algoritm to convert a monoid into an automaton [closed]

In literature, is there an algoritm to convert a monoid into an atomaton? I am looking for references/applications.
10
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1answer
187 views

Group isomorphism to graph ismorphism

In reading some blogs about computational complexity (for example here)I assimilated the notion that deciding if two groups are isomorphic is easier than testing two graphs for isomorphism. For ...
2
votes
1answer
97 views

n-Cube as a Cayley Graph

I'm taking a class on graph theory that uses "Graph Theory (Graduate Texts in Mathematics)" by Bondy and Murty. One of the questions is about Cayley graphs and the n-cube, and I don't understand how ...
8
votes
3answers
478 views

Bridge theorems for group theory and formal languages

Is there some natural or notable way to relate or link math groups and CS formal languages or some other core CS concept e.g. Turing machines? I am looking for references/applications. However ...
29
votes
6answers
4k views

What use are groups, monoids, and rings in database computations?

Why would a company like Twitter be interested in algebraic concepts like groups, monoids and rings? See their repository at github:twitter/algebird. All I could find is: Implementations of ...
3
votes
1answer
232 views

Visualized definition of cohomology

I cannot imagine how cohomology is related to graph theory, actually I read solid definition from wiki, and to be honest, I cannot understand it. e.g I know what is homotopy (in simple term), group ...