This paper combines edge technology and communication transmission control technology to characterize the translation logical synonymity of machine-automatically converted translated text, the mapping results of logical synonymity of machine-automatically converted translated text, and construct the logical synonymity model of machine-automatically translated text. Starting from the classification of synonym identification, the similarity algorithm is used to calculate the editing distance and the longest common substring of the synonymous terms of the translated text, and according to the translated text, the synonym matching items are extracted from an arbitrary text collection, and the pairing determines whether there is any synonymity in it. The analysis of data analysis involves analyzing the logical synonymity features of translated texts that use edge technology and Chinese-English and English-Chinese metaphor translation. The results show that the lexical distribution of the translated corpus based on edge technology is basically the same as that of the original Chinese language, except for the gap in the use of nouns (3.35%), verbs (5.19%), adjectives (3.21%), and pronouns (0.30%), the rest of the lexical distributions have very small gaps, and thus show an obvious trend of paradigm, which further confirms that the study of logical synonymy of text based on edge technology is Feasibility. Both explicit metaphors and borrowed metaphors are more than 20% higher in the proportion of direct translations from English to Chinese than from Chinese to English, indicating that the direct translation method is more frequently used in English to Chinese translation. This study contributes to the creation of a linguistic and culturally diverse situation and positively influences the translation process.