In SAT, do we require an assignment for arbitrary variables?











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I am reading about the Satisfiability Problem, in page (5) the author gives the following example :



$(P lor Q lor R) wedge
(bar{P} lor Q lor bar{R}) wedge
(P lor bar{Q} lor S) wedge
(bar{P} lor bar{R} lor bar{S})$



A satisfying assignement is $: P,Q,bar{R},bar{S}$.



A different assignments is $P,bar{R}$ to satisfy the four caluses. This means that $Q,S$ can be set arbitrarily to $True$ or $False$.



Do we require an assignment for all variables or we only reqiure to set variables that satisfy the input (i.e. $P,bar{R}$ discluding $Q,S$) ?



Does that mean that the satisfying assignment of $P,bar{R}$ is more efficient than $P,Q,bar{R},bar{S}$ given that it uses less variables ? Is there any resources to read about it ?



Also, given that $P,bar{R}$ satisfy the input, does that mean that we can disclude $Q,S$ from the original Boolean Formula ?










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    A truth assignment assigns values to all variables.
    – Yuval Filmus
    Nov 24 at 19:07















up vote
3
down vote

favorite
2












I am reading about the Satisfiability Problem, in page (5) the author gives the following example :



$(P lor Q lor R) wedge
(bar{P} lor Q lor bar{R}) wedge
(P lor bar{Q} lor S) wedge
(bar{P} lor bar{R} lor bar{S})$



A satisfying assignement is $: P,Q,bar{R},bar{S}$.



A different assignments is $P,bar{R}$ to satisfy the four caluses. This means that $Q,S$ can be set arbitrarily to $True$ or $False$.



Do we require an assignment for all variables or we only reqiure to set variables that satisfy the input (i.e. $P,bar{R}$ discluding $Q,S$) ?



Does that mean that the satisfying assignment of $P,bar{R}$ is more efficient than $P,Q,bar{R},bar{S}$ given that it uses less variables ? Is there any resources to read about it ?



Also, given that $P,bar{R}$ satisfy the input, does that mean that we can disclude $Q,S$ from the original Boolean Formula ?










share|cite|improve this question









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Georgie j. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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  • 2




    A truth assignment assigns values to all variables.
    – Yuval Filmus
    Nov 24 at 19:07













up vote
3
down vote

favorite
2









up vote
3
down vote

favorite
2






2





I am reading about the Satisfiability Problem, in page (5) the author gives the following example :



$(P lor Q lor R) wedge
(bar{P} lor Q lor bar{R}) wedge
(P lor bar{Q} lor S) wedge
(bar{P} lor bar{R} lor bar{S})$



A satisfying assignement is $: P,Q,bar{R},bar{S}$.



A different assignments is $P,bar{R}$ to satisfy the four caluses. This means that $Q,S$ can be set arbitrarily to $True$ or $False$.



Do we require an assignment for all variables or we only reqiure to set variables that satisfy the input (i.e. $P,bar{R}$ discluding $Q,S$) ?



Does that mean that the satisfying assignment of $P,bar{R}$ is more efficient than $P,Q,bar{R},bar{S}$ given that it uses less variables ? Is there any resources to read about it ?



Also, given that $P,bar{R}$ satisfy the input, does that mean that we can disclude $Q,S$ from the original Boolean Formula ?










share|cite|improve this question









New contributor




Georgie j. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











I am reading about the Satisfiability Problem, in page (5) the author gives the following example :



$(P lor Q lor R) wedge
(bar{P} lor Q lor bar{R}) wedge
(P lor bar{Q} lor S) wedge
(bar{P} lor bar{R} lor bar{S})$



A satisfying assignement is $: P,Q,bar{R},bar{S}$.



A different assignments is $P,bar{R}$ to satisfy the four caluses. This means that $Q,S$ can be set arbitrarily to $True$ or $False$.



Do we require an assignment for all variables or we only reqiure to set variables that satisfy the input (i.e. $P,bar{R}$ discluding $Q,S$) ?



Does that mean that the satisfying assignment of $P,bar{R}$ is more efficient than $P,Q,bar{R},bar{S}$ given that it uses less variables ? Is there any resources to read about it ?



Also, given that $P,bar{R}$ satisfy the input, does that mean that we can disclude $Q,S$ from the original Boolean Formula ?







complexity-theory reference-request satisfiability






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edited Nov 24 at 18:06





















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asked Nov 24 at 18:00









Georgie j.

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Georgie j. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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  • 2




    A truth assignment assigns values to all variables.
    – Yuval Filmus
    Nov 24 at 19:07














  • 2




    A truth assignment assigns values to all variables.
    – Yuval Filmus
    Nov 24 at 19:07








2




2




A truth assignment assigns values to all variables.
– Yuval Filmus
Nov 24 at 19:07




A truth assignment assigns values to all variables.
– Yuval Filmus
Nov 24 at 19:07










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If the truth value of a formula is determined by setting only a subset of the variables, an author might skip describing the remaining truth values. However, by definition, a truth assignment gives a value to every variable.






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    up vote
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    down vote













    If the truth value of a formula is determined by setting only a subset of the variables, an author might skip describing the remaining truth values. However, by definition, a truth assignment gives a value to every variable.






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      up vote
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      down vote













      If the truth value of a formula is determined by setting only a subset of the variables, an author might skip describing the remaining truth values. However, by definition, a truth assignment gives a value to every variable.






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        up vote
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        down vote










        up vote
        9
        down vote









        If the truth value of a formula is determined by setting only a subset of the variables, an author might skip describing the remaining truth values. However, by definition, a truth assignment gives a value to every variable.






        share|cite|improve this answer












        If the truth value of a formula is determined by setting only a subset of the variables, an author might skip describing the remaining truth values. However, by definition, a truth assignment gives a value to every variable.







        share|cite|improve this answer












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        answered Nov 24 at 19:20









        Juho

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