Algorithm
The word 'algorithm' has its roots in Latinizing the name of Muhammad ibn Musa al-Khwarizmi in a first step to "algorismus". Al-Khwārizmī (, , c. 780–850) was a Persian mathematician, astronomer, geographer, and scholar in the House of Wisdom in Baghdad, whose name means 'the native of Khwarezm', a region that was part of Greater Iran and is now in Uzbekistan.
Algorithmic program debugging
Algorithmic debugging was first developed by Ehud Shapiro during his PhD research at Yale University, as introduced in his PhD thesis, selected as a 1982 ACM Distinguished Dissertation. Shapiro implemented the method of algorithmic debugging in Prolog (a general purpose logic programming language) for the debugging of logic programs. In case of logic programs, the intended behavior of the program is a model (a set of simple true statements) and bugs are manifested as program incompleteness (inability to prove a true statement) or incorrectness (ability to prove a false statement). The algorithm would identify a false statement in the program and provide a counter-example to it or a missing true statement that it or its generalization should be added to the program. A method to handle non-termination was also developed. 
The research and development in the field of Algorithmic debugging has made major improvements over the original algorithms for debugging Prolog and other and extended the ideas to other language paradigms such as functional languages and object oriented languages.
Three decades since its introduction, algorithmic debugging is still an active field of computer science research and will probably remain so for decades as no panacea is in sight.