---
tag: MPX4Z65YVY
kind: concept
name: Viterbi semiring
sources:
  - wikipedia: en:80668537@r1358705209
    locator: Viterbi semiring
    note: adopted
    mention: wikipedia://en/80668537
    sections: [Summary]
same_as:
  wikidata: Q135921296
  wikipedia: Viterbi semiring
inventory: [4CTYG8ZYN8]
---

## Summary

The **Viterbi semiring** is a [[commutative|099E72KTF8]] semiring defined over the set of probabilities (typically the interval $[0,1]$) with *addition* operation as the maximum (*max*) and *multiplication* as the usual real multiplication. Formally, it can be denoted as a 5-tuple $(S, \oplus, \otimes, 0, 1)$ where: