determining the membership of in . Stronger reductions There are two common ways of producing reductions stronger than Turing reducibility. The first way is to limit the number and manner of oracle queries. Set is many-one reducible to if there is a total computable function such that an element is in if and only if is in . Such a function can be used to generate a Turing reduction (by computing , querying the oracle, and then interpreting the result). A truth table reduction or a weak truth table reduction must present all of its oracle queries at the same time. In a truth table reduction, the reduction also gives a boolean function (a truth table) which, when given the answers to the queries, will produce the final answer of the reduction. In a weak truth table reduction, the reduction uses the oracle answers as a basis for further computation depending on the given answers (but not using the oracle). Equivalently, a weak truth table reduction is one for which the use of the reduction is bounded by a computable function. For this reason, weak truth table reductions are sometimes called "bounded Turing" reductions. The second way to produce a stronger reducibility notion is to limit the computational resources that the program implementing the Turing reduction may use. These limits on the computational complexity of the reduction are important when studying subrecursive classes such as P. A set A is polynomial-time reducible to a set if there is a Turing reduction of to that runs in polynomial time. The concept of log-space reduction is similar. These reductions are stronger in the sense that they provide a finer distinction into equivalence classes, and satisfy more restrictive requirements than Turing reductions. Consequently, such reductions are harder to find. There may be no way to build a many-one reduction from one set to another even when a Turing reduction for the same sets exists. Weaker reductions According to the Church–Turing thesis, a Turing reduction is the most general form of an effectively calculable reduction. Nevertheless, weaker reductions are also considered. Set is said to be arithmetical in if is definable by a formula of Peano arithmetic with as a parameter. The set is hyperarithmetical in if there is a recursive ordinal such that is computable from , the α-iterated Turing jump of . The notion of relative constructibility is an important reducibility notion