Encoding Hard String Problems with Answer Set Programming

We solve the following problems with answer set programming (ASP)

• Closest String (CSP)
• Closest Substring (CSS)
• Longest Common Subsequence (LCS)
• Minimum Common String Partition (MCSP)
• Shortest Common Superstring (SCS)

Required Software

• executable clingo
• python3 package tqdm (eg. install via pip3 install tqdm)

Input Format

• All encodings expect an input in text form, where each line is interpreted as an input string.
• All strings are expected to have the same length.
• For the minimum common string partition problem, we read only the first two lines.

Usage

Runnable executables can be invoked by

• bin/shortest_superstring.py --input <FILE> computes the longest common superstring of <FILE>
• bin/closest_string.py --input <FILE> computes the closest string of
• bin/closest_string.py --input <FILE> --length <LEN> computes the closest substring of <FILE> with length <LEN>
• bin/aspsolver.py --prg <PRG> --input <FILE> computes PRG being either longest_common_subsequence or minimum_common_string_partition

If there are multiple alternative encodings to choose, there should be an option --flavor Current flavors are:

• none: Without this argument, the default (currently best) implementation will be run. This is currently due to an anonymous reviewer of CPM 2023
• --flavor cpm: use the encoding as described in the conference paper at CPM 2023

Structure

For each solution, we additionally have a brute-force implementation in the brute folder. The parameters are identical except that we have for each problem an individual executable such that the parameter --prg does not exist.

Each script in the bin folder executes a couple of commands:

• first, it translates the plain file into a clingo readable file format, which is done by one of the scripts in the translate folder.
• second, it calls clingo with the specific ASP encoding found in the encoding folder
• finally, it calls the specific decoder to extract the solution from the clingo log file. The decoders can be found in the folder decoder

A manual step-by-step execution can be done as follows for computing the closest string:

• translate/text2lp.py --input <TEXT-FILE> > <LP-FILE>
• clingo encoding/closest_string/closest_string.lp <LP-FILE> > <CLINGO-LOG>
• decode/closest_string.py --input <TEXT-FILE> --log <CLINGO-LOG>

Datasets and Examples

The used datasets can be generated or downloaded with the scripts in the gen folder.

gen/generate_datasets.sh downloads and generates the datasets used in the paper. It creates the directories

• covid19 with shuffled prefixes of the covid19 FASTA reference file
• random for the randomly generated datasets
• dssp from the Distinguishing String Selection Problem project

Sample Run

mkdir dataset
cd dataset
../gen/generate_datasets.sh
../bin/closest_string.py --input dssp/instances/g3/rand-4-50-50-10-1.txt
../bin/closest_string.py --length 3 --input random/csp/s05m07n009i1.txt
../bin/aspsolver.py --prg minimum_common_string_partition --input covid19/covid19.10.txt
../bin/aspsolver.py --prg longest_common_subsequence --input random/lcs/s02m05n022i1.txt
../bin/shortest_superstring.py --input random/scs/s02m10n008i0.txt

Examples in the Paper

The solutions to the figures in the paper can be revalidated with the files in the sample folder with the name sleeplessness.{PRG}.txt:

with ASP:

./bin/closest_string.py --input sample/sleeplessness.csp.txt
./bin/closest_string.py --length 4 --input sample/sleeplessness.css.txt
./bin/aspsolver.py --prg longest_common_subsequence --input sample/sleeplessness.lcs.txt
./bin/aspsolver.py --prg minimum_common_string_partition --input sample/sleeplessness.mcsp.txt
./bin/shortest_superstring.py --input sample/sleeplessness.scs.txt

with python implementations of the brute-force algorithms:

./brute/closest_string.py --input sample/sleeplessness.csp.txt
./brute/closest_string.py --length 4 --input sample/sleeplessness.css.txt
./brute/longest_common_subsequence.py --input sample/sleeplessness.lcs.txt
./brute/shortest_superstring.py --input sample/sleeplessness.scs.txt
./brute/minimum_common_string_partition.py --input sample/sleeplessness.mcsp.txt 

Note that the last call will take a long time to finish.

Misc

To check whether the code runs correctly, you can execute the python scripts in the test folder.

The output can be further processed by sqlplot.

Reference

The results are published at CPM'24, and can be refernces as:

Dominik Köppl. Encoding Hard String Problems with Answer Set Programming. In 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 259, pp. 17:1-17:21, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023). https://doi.org/10.4230/LIPIcs.CPM.2023.17