PPA

PPA may refer to:

Biomedical

Organizations

PPA (complexity)

PPA is a complexity class, standing for "Polynomial Parity Argument" (on a graph). Introduced by Christos Papadimitriou in 1994 (page 528), PPA is a subclass of TFNP. It is a class of search problems that can be shown to be total by an application of the handshaking lemma: any undirected graph that has a vertex whose degree is an odd number must have some other vertex whose degree is an odd number. This observation means that if we are given a graph and an odd-degree vertex, and we are asked to find some other odd-degree vertex, then we are searching for something that is guaranteed to exist (so, we have a total search problem).

PPA is defined as follows. Suppose we have a graph on whose vertices are -bit binary strings, and the graph is represented by a polynomial-sized circuit that takes a vertex as input and outputs its neighbors. (Note that this allows us to represent an exponentially-large graph on which we can efficiently perform local exploration.) Suppose furthermore that a specific vertex (say the all-zeroes vector) has an odd number of neighbors. We are required to find another odd-degree vertex. Note that this problem is in NP—given a solution it may be verified using the circuit that the solution is correct. A function computation problem belongs to PPA if it admits a polynomial-time reduction to this graph search problem. A problem is complete for the class PPA if in addition, this graph search problem is reducible to that problem.

Ḍād

Ḍād, or ṣ́ād (ض), is one of the six letters the Arabic alphabet added to the twenty-two inherited from the Phoenician alphabet (the others being ṯāʾ, ḫāʾ, ḏāl, ẓāʾ, ġayn). In name and shape, it is a variant of ṣād.

Pronunciation

The usual current pronunciation of this letter in modern Standard Arabic is the "emphatic" /d/: pharyngealized voiced alveolar stop  [dˤ] , pharyngealized voiced dental stop [d̪ˤ] or velarized voiced dental stop [d̪ˠ].

However, based on ancient descriptions of this sound, it is clear that in Qur'anic Arabic ḍ was some sort of unusual lateral sound.Sibawayh, author of the first book on Arabic grammar, explained the letter as being articulated from "between the first part of the side of the tongue and the adjoining molars". It is reconstructed by modern linguists as having been either a pharyngealized voiced alveolar lateral fricative  [ɮˤ]  or a similar affricated sound [d͡ɮˤ] or [dˡˤ]. The affricated form is suggested by loans of ḍ into Akkadian as ld or lṭ and into Malaysian as dl. However, not all linguists agree on this; the French orientalist André Roman supposes that the letter was actually a voiced emphatic alveolo-palatal sibilant /ʑˤ/, similar to the Polish ź.