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 ?
complexity-theory reference-request satisfiability
asked Nov 24 at 18:00
Georgie j.
162
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up vote
3
down vote
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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 ?
complexity-theory reference-request satisfiability
asked Nov 24 at 18:00
Georgie j.
162
2
A truth assignment assigns values to all variables.
– Yuval Filmus
Nov 24 at 19:07
add a comment |
up vote
3
down vote
favorite
up vote
3
down vote
favorite
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
asked Nov 24 at 18:00
Georgie j.
162
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
complexity-theory reference-request satisfiability
asked Nov 24 at 18:00
Georgie j.
162
asked Nov 24 at 18:00
Georgie j.
162
edited Nov 24 at 18:06
asked Nov 24 at 18:00
Georgie j.
162
asked Nov 24 at 18:00
Georgie j.
162
asked Nov 24 at 18:00
Georgie j.
162
162
2
A truth assignment assigns values to all variables.
– Yuval Filmus
Nov 24 at 19:07
add a comment |
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
add a comment |
1 Answer
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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.
answered Nov 24 at 19:20
Juho
15.1k54089
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
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.
answered Nov 24 at 19:20
Juho
15.1k54089
add a comment |
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.
answered Nov 24 at 19:20
Juho
15.1k54089
add a comment |
up vote
9
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.
answered Nov 24 at 19:20
Juho
15.1k54089
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.
answered Nov 24 at 19:20
Juho
15.1k54089
answered Nov 24 at 19:20
Juho
15.1k54089
answered Nov 24 at 19:20
Juho
15.1k54089
answered Nov 24 at 19:20
Juho
15.1k54089
15.1k54089
add a comment |
add a comment |
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2
A truth assignment assigns values to all variables.
– Yuval Filmus
Nov 24 at 19:07