Mixing
Decidability/Undecidability of feasibility of optimization problems
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I build "on top of" the posts "Is the feasibility of a system of non-convex quadratic equations and inequations decidable?" and "Is the first-order theory (with =) of real numbers with addition and multiplication complete and decidable?" My understanding is that all coefficients in question can be algebraic numbers. Question: Can the coefficients be replaced by computable real numbers? I doubt that this is the case because algebraic numbers can be specified with polynomial equalities and inequalities whereas (I think), general non-computable reals cannot. However, my knowledge is lacking and I'd be thankful for an answer.
logic
asked Feb 2 at 3:55
Mukul AgarwalMukul Agarwal
186
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add a comment |
$begingroup$
I build "on top of" the posts "Is the feasibility of a system of non-convex quadratic equations and inequations decidable?" and "Is the first-order theory (with =) of real numbers with addition and multiplication complete and decidable?" My understanding is that all coefficients in question can be algebraic numbers. Question: Can the coefficients be replaced by computable real numbers? I doubt that this is the case because algebraic numbers can be specified with polynomial equalities and inequalities whereas (I think), general non-computable reals cannot. However, my knowledge is lacking and I'd be thankful for an answer.
logic
asked Feb 2 at 3:55
Mukul AgarwalMukul Agarwal
186
$endgroup$
1
$begingroup$
If you are going to reference other posts, you should link to them. You can use the linked chain icon in the posting box, but I prefer the simpler syntax[ visible text ](address)
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– Paul Sinclair
Feb 2 at 16:43
add a comment |
$begingroup$
I build "on top of" the posts "Is the feasibility of a system of non-convex quadratic equations and inequations decidable?" and "Is the first-order theory (with =) of real numbers with addition and multiplication complete and decidable?" My understanding is that all coefficients in question can be algebraic numbers. Question: Can the coefficients be replaced by computable real numbers? I doubt that this is the case because algebraic numbers can be specified with polynomial equalities and inequalities whereas (I think), general non-computable reals cannot. However, my knowledge is lacking and I'd be thankful for an answer.
logic
asked Feb 2 at 3:55
Mukul AgarwalMukul Agarwal
186
$endgroup$
I build "on top of" the posts "Is the feasibility of a system of non-convex quadratic equations and inequations decidable?" and "Is the first-order theory (with =) of real numbers with addition and multiplication complete and decidable?" My understanding is that all coefficients in question can be algebraic numbers. Question: Can the coefficients be replaced by computable real numbers? I doubt that this is the case because algebraic numbers can be specified with polynomial equalities and inequalities whereas (I think), general non-computable reals cannot. However, my knowledge is lacking and I'd be thankful for an answer.
logic
logic
asked Feb 2 at 3:55
Mukul AgarwalMukul Agarwal
186
asked Feb 2 at 3:55
Mukul AgarwalMukul Agarwal
186
edited Feb 2 at 4:14
Mukul Agarwal
asked Feb 2 at 3:55
Mukul AgarwalMukul Agarwal
186
asked Feb 2 at 3:55
Mukul AgarwalMukul Agarwal
186
asked Feb 2 at 3:55
Mukul AgarwalMukul Agarwal
186
186
1
$begingroup$
If you are going to reference other posts, you should link to them. You can use the linked chain icon in the posting box, but I prefer the simpler syntax[ visible text ](address)
$endgroup$
– Paul Sinclair
Feb 2 at 16:43
add a comment |
1
$begingroup$
If you are going to reference other posts, you should link to them. You can use the linked chain icon in the posting box, but I prefer the simpler syntax[ visible text ](address)
$endgroup$
– Paul Sinclair
Feb 2 at 16:43
1
1
$begingroup$
If you are going to reference other posts, you should link to them. You can use the linked chain icon in the posting box, but I prefer the simpler syntax
[ visible text ](address)$endgroup$
– Paul Sinclair
Feb 2 at 16:43
$begingroup$
If you are going to reference other posts, you should link to them. You can use the linked chain icon in the posting box, but I prefer the simpler syntax
[ visible text ](address)$endgroup$
– Paul Sinclair
Feb 2 at 16:43
add a comment |
0
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$begingroup$
If you are going to reference other posts, you should link to them. You can use the linked chain icon in the posting box, but I prefer the simpler syntax
[ visible text ](address)$endgroup$
– Paul Sinclair
Feb 2 at 16:43