We study practical approximations to Kolmogorov prefix complexity (K) using IMP2, a high-level programming language. Our focus is on investigating the interpreter optimality for this language as the reference machine for the Coding Theorem Method (CTM). A method advanced to deal with applications to algorithmic complexity different to the popular traditional lossless compression approach based on the principles of algorithmic probability. The chosen model of computation is proven to be suitable for this task and a comparison to other models and methods is performed. Our findings show that CTM approximations using our model do not always correlate with results from lower-level models of computation. This suggests some models may require a larger program space to converge to Levin's universal distribution. Furthermore, we compare CTM with an upper bound to Kolmogorov complexity and find a strong correlation, supporting CTM's validity as an approximation method with finer-grade resolution of K.

翻译：本研究利用高级编程语言IMP2，对柯尔莫哥洛夫前缀复杂度（K）的实际逼近方法进行探讨。我们重点考察将该语言的解释器作为编码定理方法（CTM）参考机器时的最优性。该方法基于算法概率原理提出，用于处理算法复杂性应用，有别于传统流行的基于无损压缩的途径。研究证明所选计算模型适用于此任务，并与其他模型和方法进行了比较。我们的研究结果表明，使用本模型的CTM逼近结果并不总是与低级计算模型的结果相关。这暗示某些模型可能需要更大的程序空间才能收敛至莱文通用分布。此外，我们将CTM与柯尔莫哥洛夫复杂度的上界进行比较，发现二者存在强相关性，这支持了CTM作为具有更精细K值分辨率的逼近方法的有效性。