In SAT, do we require an assignment for arbitrary variables?
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
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.
add a comment |
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
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.
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
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
complexity-theory reference-request satisfiability
asked Nov 24 at 18:00
Georgie j.
162
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.
asked Nov 24 at 18:00
Georgie j.
162
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.
edited Nov 24 at 18:06
asked Nov 24 at 18:00
Georgie j.
162
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.
asked Nov 24 at 18:00
Georgie j.
162
asked Nov 24 at 18:00
Georgie j.
162
162
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.
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.
Georgie j. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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
1
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
15.1k54088
add a comment |
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
15.1k54088
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
15.1k54088
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
15.1k54088
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
15.1k54088
answered Nov 24 at 19:20
Juho
15.1k54088
answered Nov 24 at 19:20
Juho
15.1k54088
answered Nov 24 at 19:20
Juho
15.1k54088
15.1k54088
add a comment |
add a comment |
Georgie j. is a new contributor. Be nice, and check out our Code of Conduct.
Georgie j. is a new contributor. Be nice, and check out our Code of Conduct.
Georgie j. is a new contributor. Be nice, and check out our Code of Conduct.
Georgie j. is a new contributor. Be nice, and check out our Code of Conduct.
Thanks for contributing an answer to Computer Science Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fcs.stackexchange.com%2fquestions%2f100498%2fin-sat-do-we-require-an-assignment-for-arbitrary-variables%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
2
A truth assignment assigns values to all variables.
– Yuval Filmus
Nov 24 at 19:07