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Valley degree of freedom has attracted great interest in the realization of topological edge states in acoustic systems owing to its rich valley-contrasting physics and great potential applications. However, the practice of valley acoustic topological insulators (ATIs) in designing tunable multifunctional devices without changing their structures still remains a great challenge. Here, we show that the antisymmetric and symmetric distribution nature of valley edge states in the valley ATIs with two different domain walls can be utilized to design tunable robust acoustic logic gates (ALGs). We experimentally demonstrate two types of tunable bifunctional ALGs (denoted as ALG-I and ALG-II), in which ALG-I is composed of a single domain wall, and ALG-II is constructed by a bent topological waveguide containing two domain walls. For ALG-I, the functions of logical inclusive OR and logical exclusive OR (denoted as OR and XOR, respectively) can be switched by actively tuning the phases of two input sound sources without changing the structure. For ALG-II, the logic functions OR and XOR can be implemented through the left and right incidences, respectively, of a pair of sound sources. Similarly, the switching of the logic functions OR and XOR on both sides of ALG-II can be realized by simply adjusting the phases of two sound sources. The designed ALGs have the advantages of simple structure, high robustness, as well as active tunability, leading to a wide range of potential applications in integrated acoustics, acoustic communications, and information processing. [ABSTRACT FROM AUTHOR]