*NaPS (Nagoya pseudo-Boolean solver)* is a pseudo-Boolean solver for linear problems with Boolean variables developed based on *MiniSAT+* at Nagoya University
Linear constraint ```y1 - 3*y2 = 0``` is described as
```1 y1 -3 y2 = 0 ;```
NaPS follows MiniSAT+ for the input format, for example:
```
* #variable= 2 #constraint= 2
min: 1 x1 1 y1 ;
1 x1 -1 y1 >= 0 ;
1 x1 2 y1 <= 2 ;
```
where the first two lines are optional.
---
## Descriptions
### [Negated Boolean variable]
```~x1``` denotes the negation of ```x1``` as the following example:
```1 ~x1 2 x2 3 ~x3 = 3;```
### [facility of definition]
In addition to ordinary constraints interpreted conjunction. This solver has a facility of definition, which enables us to write complex formulas like CNFs. For example,
```d x3 => 1 x1 -2 x2 > 0 ;```
represents a constraint meaning
```x3 implies x1 - 2*x2 >0```
As another example, the following description denotes (```c1``` or ```c2```) and ((not ```c2```) or (not ```c3```)):
```
d x1 => c1 ;
d x2 <=> c2 ;
d x3 <= c3 ;
1 x1 1 x2 >= 1 ;
1 ~x2 1 ~x3 >= 1 ;
```
where in real description, ```c1```, ```c2```, and ```c3``` should be replaced by linear constraints.
### [minimization]
Minimizing goal value facility is inherited from minisatp.
e.g.
```min: 1 x1 -1 x2```
### [model counting]
Finding number of models is possible, inherited from minisatp. Projection model counting is also possible, where variables that appear in minimization goal are focused on. In this case,
minimization goal is ignored and used only for denoting a set of variables.
### [soft constraint]
Soft constraints are accepted, like
```[3] 1 y1 3 = 0```
```[3]``` shows the penalty in case of the model does not satisfy this. The solver tries to find a model with minimum sum of penalties.
## Optional input formats
### [dimacs inputs]
```-dimacs``` option enables to read dimacs cnf files.
### [maxsat mode]
```-max-sat``` option states to solve maxsat cnf/wcnf.
---
## Usage and Installation
For showing its usage, try
```naps --help```
See INSTALL for its installation.
---
## Known BUGs
* ```-S``` may result wrong answer.
* Combination of ```-Simp``` and ```-es1``` may result wrong answer.
---
## History
NaPS 1.00 is a release, renamed version of gpw-2.18, where gpw solvers are developed based on minisatp-1.0:
http://minisat.se/MiniSat+.html
We thank Niklas Een and Niklas Srensson, who developed nice platform MiniSat+.
NaPS distribution contains several SAT-solvers. NaPS invokes Glueminisat by default.
All versions of gpw-2.x and NaPS-1.x are developed by Masahiko Sakai and his colleges.
