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Despite the name "constant time", the running time does not have to be independent of the problem size, but an upper bound for the running time has to be independent of the problem size. For example, the task "exchange the values of a and b if necessary so that a ≤ b {\textstyle a\leq b} " is called constant time even though the time may ...
In particular, we have the following implications involving unsolved problems: P = NP if and only if P = PH. [7] If NP = co-NP then NP = PH. (co-NP is .) The case in which NP = PH is also termed as a collapse of the PH to the second level. The case P = NP corresponds to a collapse of PH to P.
The pH range is commonly given as zero to 14, but a pH value can be less than 0 for very concentrated strong acids or greater than 14 for very concentrated strong bases. [2] The pH scale is traceable to a set of standard solutions whose pH is established by international agreement. [3]
Given its greater H + concentration, the formula yields a lower pH value for the weak base. However, pH of bases is usually calculated in terms of the OH − concentration. This is done because the H + concentration is not a part of the reaction, whereas the OH − concentration is. The pOH is defined as:
A buffer solution is a solution where the pH does not change significantly on dilution or if an acid or base is added at constant temperature. [1] Its pH changes very little when a small amount of strong acid or base is added to it. Buffer solutions are used as a means of keeping pH at a nearly constant value in a wide variety of chemical ...
First, it can be false in practice. A theoretical polynomial algorithm may have extremely large constant factors or exponents, rendering it impractical. For example, the problem of deciding whether a graph G contains H as a minor, where H is fixed, can be solved in a running time of O(n 2), [25] where n is the number of vertices in G.
[c] [2] For example, a hypothetical weak acid having K a = 10 −5, the value of log K a is the exponent (−5), giving pK a = 5. For acetic acid, K a = 1.8 x 10 −5, so pK a is 4.7. A higher K a corresponds to a stronger acid (an acid that is more dissociated at equilibrium).
An example is the partition problem. Both weak NP-hardness and weak polynomial-time correspond to encoding the input agents in binary coding. If a problem is strongly NP-hard, then it does not even have a pseudo-polynomial time algorithm. It also does not have a fully-polynomial time approximation scheme. An example is the 3-partition problem.