Boolean XOR System Solver - Jayashree Veerendra Katti - Bog

Boolean Satisfiability (SAT)is one of the famous problem present in the field of computer science
and mathematical theory. Boolean Satisfiability can be defined as the problem of finding assignments
to the variables such that, it satisfy the given a Boolean formula. Boolean Satisfiability
problems arise in many applications such as cryptology, hardware and software verification,
reliability, artificial intelligence, decision under logic constraints, computational studies of Biological
networks. Recent application of solving Boolean systems arises in Biological
(Genetic Regulatory) Networks.
The CNF Satisfiability(CNFSAT) Problem is one of the important case of of the Satisfiability
Problem, where the Boolean formula is represented in the CNF form i.e.Conjunctive Normal
Form (CNF).This means Boolean formula is a conjunction of clauses and each clause is a disjunction
of literals. A literal is a variable or its negation.CNF SAT has central importance in
computer science. SAT normally suits to the formulas if they are in Conjunctive Normal
Form , as mentioned, should be a set of clauses.
SAT is considered as NP-complete problem in its general form. Inspite of this reality,
there are number of problems which can be successfully solved by SAT such as cryptanalysis,
bioinformatics, hardware verification, etc. For recent past twenty years the effectiveness of
SAT algorithms has significantly increased. XOR-SAT is one special case of Boolean SAT where each equation is an exclusive OR
(XOR) combination of variables. Such linear XOR systems naturally appear in problems such
as quadratic sieve method for prime factorization of numbers. Also in decoding of linear
error correction coding, linear XOR systems.In the specific case of cryptography, SAT solvers
became a very important tool to analyse and break encoding mechanisms. Within the case of
cryptanalytic application, many times SAT solvers have faced with issues that encode relatively
large amount of XOR constraints.