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5
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0answers
63 views

An Auto-Generated Cartography of Mathematical Theories: Has it been done already?

While looking for a way to visualize the logical structure of mathematical theories a graph-like depiction came to my mind, where propositions are represented by vertices. An edge goes from ...
3
votes
0answers
48 views

Using an automatic tool for checking geometric conjectures

I do a lot of research about squares, and I thought of using some automatic tool for proving / disproving some geometric conjectures. As a simple example, consider the following Square coloring ...
2
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0answers
45 views

Is it useful to learn to use automatic theorem provers?

I mean, do ATP's spot some obvious errors in computations or proofs? And if I'm not sure about the correctness of some modern proof found in some article, say for example Mochizuki's proof of the ABC ...
2
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0answers
84 views

Ordering of multisets in “Paramodulation based theorem proving”

I'm reading this paper: http://www.lsi.upc.edu/~albert/papers/handbook.ps.gz and I can't understand a part of it. it defines an ordering on multisets (it defines a multiset over $A$ as a function $A ...
1
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0answers
11 views

Status of declarative proof languages in proof assistants

I'm interested in formalising mathematics and logics in a proof assistant, both to get to know a proof assistant and to make an archive of proofs for myself (nothing too fancy, mainly first order ...
1
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0answers
56 views

Proving irregularity using Myhill-Nerode theorem

I'm trying to prove that the following language is irregular using the Myhill-Nerode theorem $$ L = \{ w\space\epsilon \{a,b,c\}^* | \#_b(w) > (\#_a(w) + \#_c(w))! \} $$ While it's completely ...
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0answers
65 views

A question about a projection of a variety

Let $\mathbb K$ be an algebraically closed field (of characteristic zero) and $H$ an irreducible variety in $\mathbb K ^n$. Let $t \in \mathbb K [x_1,\ldots,x_n]$ and let $T:= \mathsf V ( t )$ be the ...
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0answers
47 views

Cone relations and equivalence relations in the Myhill - Nerode Theorem.

Fix an alphabet ${\bf S}$ and a language $L \subset S^*$. For any two words $w$, $w'$ $\in S^*$, define a relation $w \sim w'$ if and only if Cone$(w)$ = Cone$(w')$. Then prove that this is an ...
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0answers
204 views

Coq transparency issues with type class fields

I am having some issues with, I suspect, transparency of fields in type classes. Consider a type class such as ...
0
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0answers
33 views

Why Algorithm is not is exist for understanding RE

I am reading Daniel I. Cohen book of computer theory. Here, he wrote that the recursive definition of regular Expression is easy to interpret a language, However, don't provides the way how to ...
0
votes
0answers
23 views

Computer verification of Fermat's Last Theorem - status

My question is about the status of proof verification...and specifically about Fermat's last theorem. How close are we to having computers able to verify theorems of this complexity. What about the ...