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en:research:fi-while [2016/03/22 17:57]
apeiron removed
en:research:fi-while [2018/02/16 01:25] (current)
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-FIXME **This page is not fully translated, yet. Please help completing the translation.**\\ //(remove this paragraph once the translation is finished)//+====== Title ======
  
-La version courte est disponible en cliquant {{:​fr:​recherche:​fi-while-short.pdf|ici}}.+Algorithmic Completeness of Imperative Programming Languages
  
-La version ​longue est disponible en cliquant ​{{:​fr:​recherche:​fi-while-long.pdf|ici}}.+====== Abstract ====== 
 + 
 +According to the Church-Turing Thesis, effectively calculable functions are functions computable by a Turing machine. Models that compute these functions are called Turing-complete. For example, we know that common imperative languages (such as C, Ada or Python) are Turing complete (up to unbounded memory). 
 + 
 +Algorithmic completeness is a stronger notion than Turing-completeness. It focuses not only on the input-output behavior of the computation but more importantly on the step-by-step behavior. Moreover, the issue is not limited to partial recursive functions, it applies to any set of functions. A model could compute all the desired functions, but some algorithms (ways to compute these functions) could be missing (see ((Loïc Colson: "About primitive recursive algorithms",​ Theoretical Computer Science 83 (1991) 57–69)) and ((Yiannis N. Moschovakis:​ "On Primitive Recursive Algorithms and the Greatest Common Divisor Function",​ Theoretical Computer Science (2003) ))) for examples related to primitive recursive algorithms). 
 + 
 +This paper'​s purpose is to prove that common imperative languages are not only Turing-complete but also algorithmically complete, by using the axiomatic definition of the Gurevich'​s Thesis and a fair bisimulation between the Abstract State Machines of Gurevich (defined in ((Yuri Gurevich: "​Sequential Abstract State Machines Capture Sequential Algorithms",​ ACM Transactions on Computational Logic (2000) ))) and a version ​of Jones' While programs. No special knowledge is assumed, because all relevant material will be explained from scratch. 
 + 
 +**Keywords**:​ Algorithm, ASM, Completeness,​ Computability,​ Imperative, Simulation. 
 + 
 +====== Links ====== 
 + 
 +The {{:​fr:​research:​fi-while-short.pdf|short version}} of the paper had been submitted to [[http://​fi.mimuw.edu.pl/​index.php/​FI|Fundamenta Informaticae]]. 
 + 
 +The {{:​fr:​recherche:​fi-while-long.pdf|long version}} is an older version, with very poor english and presentation,​ but contains proofs omitted in the short version.