SKIZZO & OZZIKS – QBF SOLVER AND ITS CERTIFIERLin Shuo-Ren

2012/2/1

OUTLINE

Main structure QBF solver – sKizzo

Main function Options

Reconstructor/certifier/inspector – ozziKs Main function Information dump options

MAIN STRUCTURE

MAIN FUNCTION

“.qdimacs”, “.dimacs”, “.qcnf”, and directory are acceptable

Dump useful information for certification Can modify solving process personality

Q – ground QBF reasoning S – incomplete symbolic reasoning R – complete symbolic reasoning B – DPLL-like branching reasoning G – SAT-based reasoning

Fork into two processes at very beginning, one for real job, the other measuring memory/time usage

USEFUL OPTIONS – INPUT FILE CONTROL

-dontdescend Prevent recursive processing of subdirectories

-giveup Stop solving after encounter the first unsolvable

instance In batch mode, instances will be sorted by

problem size

USEFUL OPTIONS – DUMP INFORMATION

-dump [tree, trees, TREE, TREES] Dump quantifier tree

-dump [report/flatreport] Produce a table of results

-log [text/bin] Produce an inference log recording the whole

solution process.

OZZIKS – MAIN FUNCTION

Inductive reconstruction Build a sat-certificate for QBF function

Certificate verification Certify its validity and output valid/invalid

answer Expression evaluation

Output result of the evaluation of the expression Information dump

USEFUL OPTIONS

-eval “EXP” Request the evaluation of the direct or inverse

expression EXP. -dump [qbm, exp, direxp, qbc, all] Support batch mode, too

-giveup -report

DIRECT VS. INVERSE EXPRESSION

Direct expression User provides some (partial) assignment A over

the universal variables (scenario). Then, ozziKs will produce the truth value of the expression.

Inverse expressions The user does not specify any scenario. Ask for some representation of all the scenarios

in which the expression holds.

EXAMPLES

\forall 2, 3, 5 \exist 10 .φ Direct expression

-eval “10(-2, 3, -5)” 10(-2, 3, -5) = wT

Inverse expression -eval “and(-20, or(24, 25))” and(-20, or (24, 25)) = 25% and(-20, or (24, 25)) = [25%:50%]

Multiple expressions <10, 15, 20, 21>(1, -2, 3, -5, 8) = <T, F, wF,

DC>

EXAMPLE 2

≠1

1 data

SA1 Error!

• • • inst* = data

falsedatainst inst .*trueinstdata inst .*

=1

1 data

SA1

Inst*

φ