##### Wikipedia

### RL

**RL**, **Rl** or **rl** may refer to:

### RL (complexity)

**Randomized Logarithmic-space** (**RL**), sometimes called **RLP** (Randomized Logarithmic-space Polynomial-time), is the complexity class of computational complexity theory problems solvable in logarithmic space and polynomial time with probabilistic Turing machines with one-sided error. It is named in analogy with RP, which is similar but has no logarithmic space restriction.

The probabilistic Turing machines in the definition of **RL** never accept incorrectly but are allowed to reject incorrectly less than 1/3 of the time; this is called *one-sided error*. The constant 1/3 is arbitrary; any *x* with 0 < *x* < 1 would suffice. This error can be made 2 times smaller for any polynomial *p*(*x*) without using more than polynomial time or logarithmic space by running the algorithm repeatedly.

Sometimes the name **RL** is reserved for the class of problems solvable by logarithmic-space probabilistic machines in *unbounded* time. However, this class can be shown to be equal to ** NL** using a probabilistic counter, and so is usually referred to as **NL** instead; this also shows that **RL** is contained in **NL**. **RL** is contained in ** BPL**, which is similar but allows two-sided error (incorrect accepts). **RL** contains ** L**, the problems solvable by deterministic Turing machines in log space, since its definition is just more general.

Noam Nisan showed in 1992 the weak derandomization result that **RL** is contained in ** SC**, the class of problems solvable in polynomial time and polylogarithmic space on a deterministic Turing machine; in other words, given *polylogarithmic* space, a deterministic machine can simulate *logarithmic* space probabilistic algorithms.

It is believed that **RL** is equal to **L**, that is, that polynomial-time logspace computation can be completely derandomized; major evidence for this was presented by Reingold et al. in 2005. A proof of this is the holy grail of the efforts in the field of unconditional derandomization of complexity classes. A major step forward was Omer Reingold's proof that ** SL** is equal to **L**.

### RL (singer)

**Robert "RL" Lavelle Huggar** (born April 2, 1977 in Minneapolis, Minnesota) is an American R&B singer, record producer and songwriter. He is best known for being the lead singer of the R&B group Next.