natural language for the constraint satisfaction problem (CSP). CSP refers to an important class of computational problems where, given a relational algebra and an existential sentence over this algebra, the question is to find out whether can be satisfied in . The algebra is often fixed, so that refers to the problem whose instance is only the existential sentence . It is proved that every computational problem can be formulated as for some algebra . For example, the n-coloring problem can be stated as CSP of the algebra , i.e. an algebra with elements and a single relation, inequality. The dichotomy conjecture (proved in April 2017) states that if is a finite algebra, then is either P or NP-complete. Generalizations Universal algebra has also been studied using the techniques of category theory. In this approach, instead of writing a list of operations and equations obeyed by those operations, one can describe an algebraic structure using categories of a special sort, known as Lawvere theories or more generally algebraic theories. Alternatively, one can describe algebraic structures using monads. The two approaches are closely related, with each having their own advantages. In particular, every Lawvere theory gives a monad on the category of sets, while any "finitary" monad on the category of sets arises from a Lawvere theory. However, a monad describes algebraic structures within one particular category (for example the category of sets), while algebraic theories describe structure within any of a large class of categories (namely those having finite products). A more recent development in category theory is operad theory – an operad is a set of operations, similar to a universal algebra, but restricted in that equations are only allowed between expressions with the variables, with no duplication or omission of variables allowed. Thus, rings can be described as the so-called "algebras" of some operad, but not groups, since the law duplicates the variable g on the left side and omits it on the right side. At first this may seem to be a troublesome restriction, but the payoff is that operads have certain advantages: for example, one can hybridize the concepts of ring and vector space to obtain the concept of associative algebra, but one cannot form a similar hybrid of the concepts of group and vector space. Another development is partial algebra where the operators can be partial functions. Certain partial functions can also be handled by