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Mar
17
comment Program with no intermediary states
What is your computation model? If you allow any model and provide denotational semantics, the answer is "trivially, yes": Just take the function induced by the denotational semantics. Edit: This also works with other formal semantics, e.g., small-step operational semantics or natural semantics.
Mar
13
reviewed Approve Showing a Problem Is Undecidable
Mar
13
awarded  Proofreader
Mar
13
reviewed Approve General versions of (Second part of) Fundamental Theorem of Calculus
Mar
8
comment What is the meaning of $M \models \varphi$?
That is the right interpretation.
Mar
8
answered What is the meaning of $M \models \varphi$?
Mar
5
awarded  Yearling
Feb
28
comment Given S is non-empty and sup(S)=inf(S), prove that the set S has only one element.
@MPW: I know, but I wanted to point out a gap in the proof.
Feb
28
comment Given S is non-empty and sup(S)=inf(S), prove that the set S has only one element.
A minor thing: What if $S = \varnothing$?
Feb
20
comment Knuth-Bendix completion algorithm: word problem
I'm not quite sure what you mean be "see certain structures". Are you asking how Knuth-Bendix is implemented, or do you want to know how to find the complete set of normal forms?
Feb
9
comment Buchberger's criterion to show Grobner basis for linear forms
Yes, that's the idea here.
Feb
9
comment Buchberger's criterion to show Grobner basis for linear forms
Right, scratch the "strictly". If its support is contained, you can reduce by $g$, yielding $E$ (and if you do it right, you can reduce in such a way the the leading coefficient of $D$ is reduced to zero), thereby getting a polynomial that is smaller according to the monomial ordering. By properties of the reduction, $E \in L$ again, so you can repeat the process. Because of well-foundedness, this can only happen finitely many times. What would the normal form look like, when it's in $L$?
Feb
9
comment Buchberger's criterion to show Grobner basis for linear forms
Didn't you want to show this for $k \neq l$? Anyway, if $k = l$, you have found a critical pair. Since $L$ is an ideal, certainly $D := x_l A -x_k B \in L$. By definition of $S$, there's some $g \in S$ whose support is strictly contained in that of $D$. What can you deduce from this?
Feb
9
comment Buchberger's criterion to show Grobner basis for linear forms
Note that A and B are elements of $S$, and they have different leading coefficients. Let's assume that $l<k$. So, first reduce with $A$ as long as possible. Can you then prove that the remainder is divisible by $B$?
Feb
8
revised Is this expression positive or negative
Not a question about formal languages; retagged.
Jan
31
reviewed Approve Binomial Theorem Practical Problem
Jan
31
reviewed Approve Continuous mapping between topological spaces
Dec
30
reviewed Reject Order of elements in abelian groups
Dec
7
comment Why $\langle I, J\rangle =R$ for distinct prime ideals $I$, $J$ of a principal ideal domain $R$?
You need the extra side condition $I,J \neq 0$!
Dec
6
reviewed Reviewed find the extremal of a function