Boolean XOR System Solver

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.