Mathematical theorems in theoretical computer science are formal statements that have been proven based on a set of axioms and definitions within the realm of computer science. They often involve concepts from mathematics, logic, algorithms, complexity, automata theory, and other related fields. Theorems are essential for establishing foundational principles and for understanding the limits of computation.
In the theory of computation, theorems are mathematical propositions that have been proven to be true based on previously established axioms and other theorems. This area of theoretical computer science deals with the fundamental aspects of computation, including what problems can be computed (computability), how efficiently they can be solved (complexity), and the limits of computation.
The Immerman–Szelepcsényi theorem is a result in computational complexity theory that establishes a relationship between two significant complexity classes: **NL** (nondeterministic logarithmic space) and **co-NL** (the complement of NL). Specifically, the theorem proves that these two classes are equal, i.e., \[ \text{NL} = \text{co-NL}.
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