Concepts inExponential space complete problems for Petri nets and commutative semigroups (Preliminary Report)

Special classes of semigroups

In mathematics, a semigroup is a nonempty set together with an associative binary operation. A special class of semigroups is a class of semigroups satisfying additional properties or conditions. Thus the class of commutative semigroups consists of all those semigroups in which the binary operation satisfies the commutativity property that ab = ba for all elements a and b in the semigroup.  more from Wikipedia

Finite set

In mathematics, a finite set is a set that has a finite number of elements. For example, is a finite set with five elements. The number of elements of a finite set is a natural number, and is called the cardinality of the set. A set that is not finite is called infinite. For example, the set of all positive integers is infinite: Finite sets are particularly important in combinatorics, the mathematical study of counting.  more from Wikipedia

Decidability (logic)

In logic, the term decidable refers to the decision problem, the question of the existence of an effective method for determining membership in a set of formulas, or, more precisely, an algorithm that can and will return a Boolean true or false value (instead of looping indefinitely). Logical systems such as propositional logic are decidable if membership in their set of logically valid formulas (or theorems) can be effectively determined.  more from Wikipedia

Algebraic group

In algebraic geometry, an algebraic group (or group variety) is a group that is an algebraic variety, such that the multiplication and inverse are given by regular functions on the variety. In category theoretic terms, an algebraic group is a group object in the category of algebraic varieties.  more from Wikipedia

Ideal (ring theory)

In ring theory, a branch of abstract algebra, an ideal is a special subset of a ring. The ideal conceptually generalizes the property of certain subsets of the integers, such as the "even numbers" or "multiples of 3", that the product of any element of the ring with an element of the subset is again in the subset: the product of any integer with an even integer is again an even integer. An ideal is therefore said to absorb the elements of the ring under multiplication.  more from Wikipedia

Polynomial

In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents. For example, x − x/4 + 7 is a polynomial, but x − 4/x + 7x is not, because its second term involves division by the variable x (4/x), and also because its third term contains an exponent that is not an integer (3/2).  more from Wikipedia

Petri net

A Petri net (also known as a place/transition net or P/T net) is one of several mathematical modeling languages for the description of distributed systems. A Petri net is a directed bipartite graph, in which the nodes represent transitions (i.e. events that may occur, signified by bars) and places (i.e. conditions, signified by circles). The directed arcs describe which places are pre- and/or postconditions for which transitions (signified by arrows).  more from Wikipedia

Classical mechanics

In physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces. The study of the motion of bodies is an ancient one, making classical mechanics one of the oldest and largest subjects in science, engineering and technology.  more from Wikipedia