Some textbooks[1] and published research literature might define an anticausal system to be one that does not depend on past input values, allowing also for the dependence on present input values.
This is in contrast to a causal system which depends only on current and/or past input values.
[2] This is often a topic of control theory and digital signal processing (DSP).
An acausal system that has any dependence on past input values is not anticausal.
Digital room correction in some sound reproduction systems rely on acausal filters.