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







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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)
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    – Paul Sinclair
    Feb 2 at 16:43
















0












$begingroup$


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







share|cite|improve this question











$endgroup$








  • 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)
    $endgroup$
    – Paul Sinclair
    Feb 2 at 16:43














0












0








0





$begingroup$


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







share|cite|improve this question











$endgroup$




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






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share|cite|improve this question













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edited Feb 2 at 4:14







Mukul Agarwal

















asked Feb 2 at 3:55









Mukul AgarwalMukul Agarwal

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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














  • 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










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