Multiset Constraint Solver for Multi-SAT
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MANIFEST
Multiset_Constraint_Solving_and_Its_Applications.pdf
README.md
ms
setup.cfg
setup.py

README.md

msat

=====

Environments

Python

You have to install Python3.


How to get msat

Just download from github tarball:

User also can install msat from pip (Python3 Version, sometimes called pip3):

$ pip install msat

If there is new version, use upgrade:

$ pip install msat --upgrade

Here is the pypi page of msat:

Note that if you install msat from pip, you will not get benches here.


Run msat

If you do not install the packages and script, just cd to the top directory:

$ ./ms

If you have already installed it, just type ms:

$ ms

You will see following info:

msat:
    python3 ms <CMD> [OBJECTS & OPTIONS]
            ms <CMD> [OBJECTS & OPTIONS]
          ./ms <CMD> [OBJECTS & OPTIONS]
    If this is your first use, please run configure!
CMD:
    cmd          : list all avalible commands and their short usage
    configure    : setting enviroments
    help         : show the full infomation of a command
    setdiff      : diff the default settings and the local settings
    solve        : solve a mc problem

The format of ms command is:

ms <CMD> [OBJECTS & OPTIONS]

ms is the main script name.
CMD is the msat command.
OBJECTS & OPTIONS are options or target objects of the corresponding "CMD".


List commands and get help

We can use "cmd" to list all avalible msat commands:

CMD:
    cmd          : list all avalible commands and their short usage
    configure    : setting enviroments
    help         : show the full infomation of a command
    setdiff      : diff the default settings and the local settings
    solve        : solve a mc problem

If we want to know the details of a specific command, just use msat command help:

$ ms help solve

    USAGE: solve a mc problem
    SYNOPSIS:
        solve [-i] <mc file> [-o <result file>]
    OPTIONS:
        -i : intelligent setting
        -o : result file name

USAGE gives a brief description of this command.
SYNOPSIS gives the format of this command.
OPTIONS gives descriptions of all avalible options.

For example, if you want to use command solve for solving a multiset constraint problem (written in standard mc file format named example.mc) with default settings (that means you don't need to use any options), just type:

$ ms solve example.mc

Note that, if there is nothing happeded, please run configure first!

Configure

If this is your first use, please run configure!

$ ms configure

You will see local_settings.py in your current directory. Congrats! Configure is succesful! Now the solve command is avalible in this directory.


Solve a multiset constraint problem

First, you should have a standard mc file for describing the multiset constraint problem with some user-specified settings.

Standard file format of multiset constraint problem

Let's see following example:

# example.mc
e 5 6 18 44 12 3 33 11 45
e 7 9 8 10 8 11 32 15 23 24 1 1 2 2 4 6 8 4 55 12 79 86 12 15 16 33 12 13
t 11 74 36 56 15 9
t 10 8 43 15 47 2 14 12 67 79 98 31 45 13 2
r =
s PROGRESS = False
s ELEMENTS_ORDER = 'increase' # increase/decrease/no
s TARGETS_ORDER = 'increase'  # increase/decrease/no

It is a standard-format file of a multiset constraint problem.
User should use e, t, r, s, and # as the first non-blank char of a line.

We call these chars as "line keyword":

  • keyword e is used to specify elements (element set).
  • Keyword t is used to specify targets (target set).
  • Keyword r is used to specify the relation between multi-subset and its corresponding target.
  • Keyword s is used to do solver settings for a specific multiset constraint problem.
  • Keyword, # is used to write down comments.

Note that we could use multiple "e lines" and "t lines" to describe element set and target set respectively. Also, the setting statements are allowed with comment.

Solve it

Solve a multiset constraint file (mc file) is easy. Use command solve:

$ ms solve example.mc

Log and log file

Let's introduce the log of solving. Take above mc problem as example, the log is like following:

================================================================================
|               MSAT - Multiset Constraint Solver for Multi-SAT                |
================================================================================
| % MC file             : example.mc                                           |
| % Elements (Num:37)   : [5, 6, 18, 44, 12, 3, 33, 11, 45, 7, 9, 8, ... more  |
| % Targets  (Num:21)   : [11, 74, 36, 56, 15, 9, 10, 8, 43, 15, 47, ... more  |
| % Relation            : =                                                    |
--------------------------------------------------------------------------------
|                       Mc Settings specified in Mc File                       |
--------------------------------------------------------------------------------
| S TARGETS_ORDER = 'increase'         || S ELEMENTS_ORDER = 'increase'        |
| S PROGRESS = False                   ||                                      |
--------------------------------------------------------------------------------
|             Mc Settings Specified in Mc File and Intelligent Setting         |
--------------------------------------------------------------------------------
| % Table Size          : 38*686 = 26068                                       |
| % Elements Order      : increase                                             |
| % J-range Min         : False                                                |
| % Build Time          : 0.13407                                              |
--------------------------------------------------------------------------------
|                         Multiset Constraint Solving                          |
--------------------------------------------------------------------------------
| % Satisfiability      : False                                                |
| % Solving Time        : 0.00018                                              |
--------------------------------------------------------------------------------
|                              Profiling Summary                               |
--------------------------------------------------------------------------------
| % backtrack_num       : 1                                                    |
| % check_sum_fail_num  : 1                                                    |
| % check_sum_comb_fail_num: 0                                                 |
| % check_distance_fail_num: 0                                                 |
| % forbiden_combination_num: 0                                                |
================================================================================

First, solver lists the basic info of the multiset constraint problem including the file's name, elements (and it's number), targets (and it's number) and the relation.

Then the settings specified in the MC file are listed. Solver doesn't show the default settings in settings.py.

The next block shows the info of MC table and MC dictionary including:

  • Table size: with the form of row number X column number = table entry number
  • Elements order: the order of elements for building the table and dictionary.
  • J-range min: this value is True if solver minimizes the column size.
  • Build Time: cost time for building the table and dictionary.

When solving is finished, solver will show the satisfiability of this MC problem and the solving time.

Finally, the profiling summary is given.

If you want to dump the log in to a file, just use redirection:

$ ms solve example.mc > example.log

Result file

If this mc problem is SAT(satisfiable). That means solver finds several suitable multi-subsets that can satisfy all of the targets. So solver writes down the result for showing detail. This result is named <mc file name>.result. For example, the result file name of "example.mc" is "example.mc.result".

Result file is a json file:

[
  {
    "elements":[
      3,  
      1   
    ],  
    "target":4
  },  
  {
    "elements":[
      3,  
      1   
    ],  
    "target":4
  }
]

User can specify the name of result file by using -o option:

$ ms solve example.mc -o Myresult

Settings

We can modify the solver settings by editing settings.py in msat module directory or local_settings.py in the current directory. Of course, user can specifiy the problem-concerned settings in MC file for specific MC problem.

Note that the settings in MC file cover the settings in local_settings.py and the settings in local_settings.py cover the settings in settings.py. If you want to know the differences between settings.py and loca_settings.py, use command setdiff to help us:

$ ms setdiff

Let me introduce all avalible solver settings to you.

Solver display

There are two width param for us to modify the size of log window.

  • SOLVER_WIDTH

    • width of solver window
    • is an even
  • SOLVER_ITEM_WIDTH

    • width of an item name like "Table Size" or "Satisfiability"
    • is an positive integer
SOLVER_WIDTH = 80 # should be even
SOLVER_ITEM_WIDTH = 20

MC table

When solver constructs the MC table, it fix the orders of element set and target set first.

  • ELEMENTS_ORDER

    • order of elements for building the MC table
    • 3 strings are allowed: 'increase', 'decrease' and 'no'
    • for example, elements set = (2, 4, 5, 1, 3)
      • use increase => elements list = [1, 2, 3, 4, 5]
      • use decrease => elements list = [5, 4, 3, 2, 1]
      • use no => elements list = [2, 4, 5, 1, 3] (original order)
  • TARGETS_ORDER

    • order of targets for building the MC table
    • this order just affects the choose process
    • 3 strings are allowed: 'increase', 'decrease' and 'no' (the meaning just as ELEMENTS_ORDER)

When building MC table, we could decide whether minize the column number of MC table. If the value is true, we could build a smaller MC table with less memory use and less building time. But set this value True can speed up the searching time when quering value of MC table.

  • JRANGE_MIN
    • is a boolean value
ELEMENTS_ORDER = 'increase' # increase/decrease/no
TARGETS_ORDER = 'increase'  # increase/decrease/no
JRANGE_MIN = False

Search

We call the solving process of traveling in the solution space "search". There are many strategy we could use in this stage. Sometimes modifying a param results in a big variation of solving time.

When doing search, solver tries to choose a target (or choose nothing) picking row element in each level. The strategy of choose can decided by user.

  • CHOOSE_NOUSE_FIRST

    • let solver try to choose nothing first
    • is a boolean value
  • CHOOSE_FROM_MAX_OR_MIN

    • let solver try to choose target with max(min) current value first
    • 3 strings are allowed: 'max', 'min' and 'no'
    • for example, current values of all targets are [1, 2, 3, 4, 5]
      • use max => try to choose from 5 to 1
      • use min => try to choose from 1 to 5
      • use no => use the original order for choosing
CHOOSE_NOUSE_FIRST = False
CHOOSE_FROM_MAX_OR_MIN = 'max' # max/min/no

Sometimes, other constraint is needed for special MC problem type.

  • ALL_USE_RULE
    • all elements should be used by taregts when this param is turned on
    • is a boolean value
ALL_USE_RULE = False

Search process finishes when solver propagates to the first row of MC table defaultly. But in fact, when all targets go into the all true region, the satisfiability is comfirmed as True. We allowed user to turn on this optional check. Note that this check is a time-consuming behavior.

  • EARLY_CHECK_SATISFIABILITY
    • check satisfiability in each level
    • is a boolean value
EARLY_CHECK_SATISFIABILITY = False

When doing search, we can do a early backtracking by early backtrack checking (find the conflict in early time). There are several additional check for early backtrack.

  • CHECK_FOR_EARLY_BACKTRACK

    • turn off this param blocks all kinds of early backtrack check
    • is a boolean value
  • CHECK_SUM

    • check sum of current values of all targets in each level
    • is a boolean value
  • CHECK_SUM_COMB

    • check sum of current values of targets in several combination in each level
    • the size of each combination is specified by param CHECK_SUM_COMB_NUM
    • is a boolean value
  • CHECK_SUM_COMB_NUM

    • check sum of current values of several targets in each level
    • is a positive integer which is greater than 1
  • CHECK_DISTANCES

    • check the distances between current targets and first False value they will encounter
    • is a boolean value
  • CHECK_FORBIDEN

    • check whether the current target set is a forbiden combination
    • is a boolean value
CHECK_FOR_EARLY_BACKTRACK = True
CHECK_SUM = True
CHECK_SUM_COMB = True
CHECK_SUM_COMB_NUM = 6
CHECK_DISTANCES = True
CHECK_FORBIDEN = True

Progress

Turn on the progress param, user can get the solving progress like following:

Progress of building MC table
--------------------------------------------------------------------------------
|                           MC Table & MC Dictionary                           |
--------------------------------------------------------------------------------
| % Table Size          : 89*8193 = 729177                                     |
| % Elements Order      : increase                                             |
| % J-range Min         : False                                                |
| P Build MC Table      : [=======>                                   ] 19.04 %|
Progress of searching solution space

This progress does'nt point out the solving progress, just tells us the traversed percentage of the solution space.

--------------------------------------------------------------------------------
|                         Multiset Constraint Solving                          |
--------------------------------------------------------------------------------
| P Search Sol Space    : [>                                          ] 0.00  %|
  • PROGRESS
  • turn on this param for getting the solving progress
  • it cost much times
  • is a boolean value
PROGRESS = False

Profiling

We could use PROFILING_COUNT to do the counting for profiling, and PROFILING_SUMMARY let solver print the result of profiling.

  • PROFILING_COUNT

    • do the counting for profiling
    • is a boolean value
  • PROFILING_SUMMARY

    • let solver print the result of profiling
    • only list the variables specified in tuple param PROFILING_VARS
    • is a boolean value
  • PROFILING_VARS

    • specify the variables shown in the profiling summary
    • is string tuple
    • solver supports 5 vars now including:
      • 'backtrack_num'
      • 'check_sum_fail_num'
      • 'check_sum_comb_fail_num'
      • 'check_distance_fail_num'
      • 'forbiden_combination_num'
PROFILING_VARS = (
    'backtrack_num',
    'check_sum_fail_num',
    'check_sum_comb_fail_num',
    'check_distance_fail_num',
    'forbiden_combination_num'
)

PROFILING_COUNT = True
PROFILING_SUMMARY = True

Output subset

  • OUTPUT SUBSET
    • turn on for outputing the result file when satisfiability is True
    • is a boolean value
OUTPUT_SUBSET = True

Debug

Here are some debug params:

  • DEBUG_TITLE

    • turn on for printing debug title
    • is a boolean value
  • DEBUG_MSG

    • turn on for printing debug message
    • is a boolean value
  • DEBUG_INTERUPT

    • turn on for doing search step by step (action by action)
    • is a boolean value
  • DEBUG_SHOW_SEARCH_STATUS

    • turn on for printing search status for each search action
    • is a boolean value
DEBUG_TITLE = False
DEBUG_MSG = False
DEBUG_INTERUPT = False
DEBUG_SHOW_SEARCH_STATUS = False

Intelligent Setting

Different MC problems have their unique properties. And solver settings really affects the solving efficiency according to these properties. Intelligent setting is a building feature of msat! Let msat decide the final settings to help you solving the problem more efficiently. Just use -i option with command solve:

$ ms solve -i example.mc

and intelligent settings will be listed in the log file:

--------------------------------------------------------------------------------
|           Mc Settings Specified in Mc File and Intelligent Setting           |
--------------------------------------------------------------------------------
| I CHOOSE_FROM_MAX_OR_MIN = min       || I ELEMENTS_ORDER = increase          |
| S TARGETS_ORDER = 'increase'         || S ELEMENTS_ORDER = 'increase'        |
| S PROGRESS = False                   ||                                      |

The items starts with 'I' are the intelligent settings.