Matrices inducing generalized metric on sequences

Sequence comparison is a basic task to capture similarities and differences between two or more sequences of symbols, with countless applications such as in computational biology. An alignment way compare sequences, where giving scoring function determines the degree similarity them. Many functions are obtained from matrices. However,not all matrices induce which distances, since not necessarily metric. In this work we establish necessary sufficient conditions for each one properties metric weighted edit distances. For subset that normalized also characterize class inducing Furthermore, define an extended distance, takes into account set editing operations transforms sequence another regardless existence usual corresponding represent them, describing criterion find whose weight minimum. Similarly, determine induces distances