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 :



$(P lor Q lor R) wedge
(barP lor Q lor barR) wedge
(P lor barQ lor S) wedge
(barP lor barR lor barS)$



A satisfying assignement is $: P,Q,barR,barS$.



A different assignments is $P,barR$ 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. $P,barR$ discluding $Q,S$) ?



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



Also, given that $P,barR$ 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 :



$(P lor Q lor R) wedge
(barP lor Q lor barR) wedge
(P lor barQ lor S) wedge
(barP lor barR lor barS)$



A satisfying assignement is $: P,Q,barR,barS$.



A different assignments is $P,barR$ 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. $P,barR$ discluding $Q,S$) ?



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



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










share|cite|improve this question



















  • 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 :



$(P lor Q lor R) wedge
(barP lor Q lor barR) wedge
(P lor barQ lor S) wedge
(barP lor barR lor barS)$



A satisfying assignement is $: P,Q,barR,barS$.



A different assignments is $P,barR$ 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. $P,barR$ discluding $Q,S$) ?



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



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










share|cite|improve this question















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



$(P lor Q lor R) wedge
(barP lor Q lor barR) wedge
(P lor barQ lor S) wedge
(barP lor barR lor barS)$



A satisfying assignement is $: P,Q,barR,barS$.



A different assignments is $P,barR$ 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. $P,barR$ discluding $Q,S$) ?



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



Also, given that $P,barR$ 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

























asked Nov 24 at 18:00









Georgie j.

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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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    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

        15.1k54089




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