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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)// | + | ====== Abstract ====== |
| - | La version courte est disponible en cliquant {{:fr:recherche:fi-while-short.pdf|ici}}. | + | 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). |
| - | La version longue est disponible en cliquant {{:fr:recherche:fi-while-long.pdf|ici}}. | + | 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). |
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| + | 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. | ||
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| + | **Keywords**: Algorithm, ASM, Completeness, Computability, Imperative, Simulation. | ||
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| + | ====== Links ====== | ||
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| + | 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]]. | ||
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| + | 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. | ||