Can LLMs Compress (and Decompress)? Evaluating Code Understanding and Execution via Invertibility

LLMs demonstrate strong performance on code benchmarks, yet consistent reasoning across forward and backward execution remains elusive. We present RoundTripCodeEval (RTCE), a benchmark of four code execution reasoning tasks that evaluates round-trip consistency through execution-free, exact-match assessment of bijection fidelity across four lossless compression algorithms. We evaluate state-of-the-art Code-LLMs under zero-shot prompting, supervised fine-tuning on execution traces, and iterative self-reflection. All approaches yield only modest improvements and none closes the gap, revealing that current LLMs lack the internal coherence required for reliable bidirectional code reasoning. RTCE surfaces findings invisible to existing benchmarks: models frequently pass individual forward and backward tasks yet fail the combined round-trip, exposing mutually inconsistent internal representations; SFT and self-reflection saturate after one revision round, indicating they cannot repair fundamental algorithmic misunderstandings; and failures persist even on simple bijections such as RLE, suggesting that algorithmic complexity is not the sole root cause.\footnote{Code and dataset are available at https://github.com/Nickil21/round-trip-code-compression.