Counting models satisfying a boolean formulaProve NP-completeness of deciding satisfiability of monotone...
Are relativity and doppler effect related?
Are ETF trackers fundamentally better than individual stocks?
What is a ^ b and (a & b) << 1?
Bacteria contamination inside a thermos bottle
How do you talk to someone whose loved one is dying?
How could a scammer know the apps on my phone / iTunes account?
Professor being mistaken for a grad student
How to deal with taxi scam when on vacation?
Are all passive ability checks floors for active ability checks?
What is the Japanese sound word for the clinking of money?
How are passwords stolen from companies if they only store hashes?
Is a party consisting of only a bard, a cleric, and a warlock functional long-term?
Official degrees of earth’s rotation per day
Brexit - No Deal Rejection
Why did it take so long to abandon sail after steamships were demonstrated?
Aluminum electrolytic or ceramic capacitors for linear regulator input and output?
New passport but visa is in old (lost) passport
Why does a Star of David appear at a rally with Francisco Franco?
What is the purpose or proof behind chain rule?
I got the following comment from a reputed math journal. What does it mean?
Did Ender ever learn that he killed Stilson and/or Bonzo?
Can I use USB data pins as power source
PTIJ: Who should I vote for? (21st Knesset Edition)
"of which" is correct here?
Counting models satisfying a boolean formula
Prove NP-completeness of deciding satisfiability of monotone boolean formulaHow to represent a 0-valid boolean formula?What is wrong with this seeming contradiction with a paper about AND-compression of SAT?Why do we care about random Boolean SAT formula?What does a square mean in a Boolean formulaUnrolling closures into SAT boolean formulaEfficient alternatives to inclusion-exclusionCounting (enumerating) minimal solutions of a dual horn formulan-DNF boolean formula k satisfiabilityCalculating the number of assignments satisfying a general propositional formula
$begingroup$
I'm trying to implement the #2-SAT algorithm from the paper "Counting Satisfying Assignments in 2-SAT and 3-SAT" (Dahllöf, Jonsson and Wahlström, Theor. Comput. Sci. 332(1–3):265–291, 2005). A few lines into the algorithm description the authors denotes a sub algorithm and claims "The function $C_E$ computes #2-SAT by exhaustive search. It will be applied only to formulas of size ≤ 4 and can thus be safely assumed to run in O(1) time". The size of formulas is referred to the number of clauses.
I've been trying to find this exhaustive search algorithm that computes a #2-sat instance with number of clauses less than 4. But the results only returns algorithms for generally solving/counting models for #2 or #3-SAT and does not talk about a special case when size ≤ 4. First of all, is this claim true? Since the paper was published by a well known journal, I guess it is. But if so, does anyone know about this special case?
combinatorics satisfiability 2-sat
edited 4 hours ago
David Richerby
68.4k15103194
asked 5 hours ago
Rikard OlssonRikard Olsson
1082
New contributor
Rikard Olsson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
I'm trying to implement the #2-SAT algorithm from the paper "Counting Satisfying Assignments in 2-SAT and 3-SAT" (Dahllöf, Jonsson and Wahlström, Theor. Comput. Sci. 332(1–3):265–291, 2005). A few lines into the algorithm description the authors denotes a sub algorithm and claims "The function $C_E$ computes #2-SAT by exhaustive search. It will be applied only to formulas of size ≤ 4 and can thus be safely assumed to run in O(1) time". The size of formulas is referred to the number of clauses.
I've been trying to find this exhaustive search algorithm that computes a #2-sat instance with number of clauses less than 4. But the results only returns algorithms for generally solving/counting models for #2 or #3-SAT and does not talk about a special case when size ≤ 4. First of all, is this claim true? Since the paper was published by a well known journal, I guess it is. But if so, does anyone know about this special case?
combinatorics satisfiability 2-sat
edited 4 hours ago
David Richerby
68.4k15103194
asked 5 hours ago
Rikard OlssonRikard Olsson
1082
New contributor
Rikard Olsson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
I'm trying to implement the #2-SAT algorithm from the paper "Counting Satisfying Assignments in 2-SAT and 3-SAT" (Dahllöf, Jonsson and Wahlström, Theor. Comput. Sci. 332(1–3):265–291, 2005). A few lines into the algorithm description the authors denotes a sub algorithm and claims "The function $C_E$ computes #2-SAT by exhaustive search. It will be applied only to formulas of size ≤ 4 and can thus be safely assumed to run in O(1) time". The size of formulas is referred to the number of clauses.
I've been trying to find this exhaustive search algorithm that computes a #2-sat instance with number of clauses less than 4. But the results only returns algorithms for generally solving/counting models for #2 or #3-SAT and does not talk about a special case when size ≤ 4. First of all, is this claim true? Since the paper was published by a well known journal, I guess it is. But if so, does anyone know about this special case?
combinatorics satisfiability 2-sat
edited 4 hours ago
David Richerby
68.4k15103194
asked 5 hours ago
Rikard OlssonRikard Olsson
1082
New contributor
Rikard Olsson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I'm trying to implement the #2-SAT algorithm from the paper "Counting Satisfying Assignments in 2-SAT and 3-SAT" (Dahllöf, Jonsson and Wahlström, Theor. Comput. Sci. 332(1–3):265–291, 2005). A few lines into the algorithm description the authors denotes a sub algorithm and claims "The function $C_E$ computes #2-SAT by exhaustive search. It will be applied only to formulas of size ≤ 4 and can thus be safely assumed to run in O(1) time". The size of formulas is referred to the number of clauses.
I've been trying to find this exhaustive search algorithm that computes a #2-sat instance with number of clauses less than 4. But the results only returns algorithms for generally solving/counting models for #2 or #3-SAT and does not talk about a special case when size ≤ 4. First of all, is this claim true? Since the paper was published by a well known journal, I guess it is. But if so, does anyone know about this special case?
combinatorics satisfiability 2-sat
combinatorics satisfiability 2-sat
edited 4 hours ago
David Richerby
68.4k15103194
asked 5 hours ago
Rikard OlssonRikard Olsson
1082
New contributor
Rikard Olsson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 4 hours ago
David Richerby
68.4k15103194
asked 5 hours ago
Rikard OlssonRikard Olsson
1082
New contributor
Rikard Olsson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 4 hours ago
David Richerby
68.4k15103194
edited 4 hours ago
David Richerby
68.4k15103194
edited 4 hours ago
David Richerby
68.4k15103194
68.4k15103194
asked 5 hours ago
Rikard OlssonRikard Olsson
1082
New contributor
Rikard Olsson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 5 hours ago
Rikard OlssonRikard Olsson
1082
asked 5 hours ago
Rikard OlssonRikard Olsson
1082
1082
New contributor
Rikard Olsson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Rikard Olsson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Rikard Olsson 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 |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
For any fixed $k$, a $k$-CNF with at most four clauses has at most $4k$ variables. So you can count the satisfying assigments with
count = 0
j = number of variables
for v1 = 0 to 1 do
for v2 = 0 to 1 do
...
for vj = 0 to 1 do
if formula_value(phi, v1, ..., vj) == true
count = count + 1
This runs in time $Theta(2^j) = O(2^k) = Theta(1)$, since $k$ is fixed.
answered 4 hours ago
David RicherbyDavid Richerby
68.4k15103194
$endgroup$
$begingroup$
Wow, thanks man!!
$endgroup$
– Rikard Olsson
4 hours ago
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "419"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Rikard Olsson is a new contributor. Be nice, and check out our Code of Conduct.
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%2f105674%2fcounting-models-satisfying-a-boolean-formula%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
For any fixed $k$, a $k$-CNF with at most four clauses has at most $4k$ variables. So you can count the satisfying assigments with
count = 0
j = number of variables
for v1 = 0 to 1 do
for v2 = 0 to 1 do
...
for vj = 0 to 1 do
if formula_value(phi, v1, ..., vj) == true
count = count + 1
This runs in time $Theta(2^j) = O(2^k) = Theta(1)$, since $k$ is fixed.
answered 4 hours ago
David RicherbyDavid Richerby
68.4k15103194
$endgroup$
$begingroup$
Wow, thanks man!!
$endgroup$
– Rikard Olsson
4 hours ago
add a comment |
$begingroup$
For any fixed $k$, a $k$-CNF with at most four clauses has at most $4k$ variables. So you can count the satisfying assigments with
count = 0
j = number of variables
for v1 = 0 to 1 do
for v2 = 0 to 1 do
...
for vj = 0 to 1 do
if formula_value(phi, v1, ..., vj) == true
count = count + 1
This runs in time $Theta(2^j) = O(2^k) = Theta(1)$, since $k$ is fixed.
answered 4 hours ago
David RicherbyDavid Richerby
68.4k15103194
$endgroup$
$begingroup$
Wow, thanks man!!
$endgroup$
– Rikard Olsson
4 hours ago
add a comment |
$begingroup$
For any fixed $k$, a $k$-CNF with at most four clauses has at most $4k$ variables. So you can count the satisfying assigments with
count = 0
j = number of variables
for v1 = 0 to 1 do
for v2 = 0 to 1 do
...
for vj = 0 to 1 do
if formula_value(phi, v1, ..., vj) == true
count = count + 1
This runs in time $Theta(2^j) = O(2^k) = Theta(1)$, since $k$ is fixed.
answered 4 hours ago
David RicherbyDavid Richerby
68.4k15103194
$endgroup$
For any fixed $k$, a $k$-CNF with at most four clauses has at most $4k$ variables. So you can count the satisfying assigments with
count = 0
j = number of variables
for v1 = 0 to 1 do
for v2 = 0 to 1 do
...
for vj = 0 to 1 do
if formula_value(phi, v1, ..., vj) == true
count = count + 1
This runs in time $Theta(2^j) = O(2^k) = Theta(1)$, since $k$ is fixed.
answered 4 hours ago
David RicherbyDavid Richerby
68.4k15103194
answered 4 hours ago
David RicherbyDavid Richerby
68.4k15103194
answered 4 hours ago
David RicherbyDavid Richerby
68.4k15103194
answered 4 hours ago
David RicherbyDavid Richerby
68.4k15103194
68.4k15103194
$begingroup$
Wow, thanks man!!
$endgroup$
– Rikard Olsson
4 hours ago
add a comment |
$begingroup$
Wow, thanks man!!
$endgroup$
– Rikard Olsson
4 hours ago
$begingroup$
Wow, thanks man!!
$endgroup$
– Rikard Olsson
4 hours ago
$begingroup$
Wow, thanks man!!
$endgroup$
– Rikard Olsson
4 hours ago
add a comment |
Rikard Olsson is a new contributor. Be nice, and check out our Code of Conduct.
Rikard Olsson is a new contributor. Be nice, and check out our Code of Conduct.
Rikard Olsson is a new contributor. Be nice, and check out our Code of Conduct.
Rikard Olsson 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.
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%2f105674%2fcounting-models-satisfying-a-boolean-formula%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
