In this paper we examine the neurobiological correlates of syntax, the processing of structured sequences, by comparing FMRI results on artificial and natural language syntax. We discuss these and similar findings in the context of formal language and computability theory. We used a simple right-linear unification grammar in an implicit artificial grammar learning paradigm in 32 healthy Dutch university students (natural language FMRI data were already acquired for these participants). We predicted that artificial syntax processing would engage the left inferior frontal region (BA 44/45) and that this activation would overlap with syntax-related variability observed in the natural language experiment. The main findings of this study show that the left inferior frontal region centered on BA 44/45 is active during artificial syntax processing of well-formed (grammatical) sequence independent of local subsequence familiarity. The same region is engaged to a greater extent when a syntactic violation is present and structural unification becomes difficult or impossible. The effects related to artificial syntax in the left inferior frontal region (BA 44/45) were essentially identical when we masked these with activity related to natural syntax in the same subjects. Finally, the medial temporal lobe was deactivated during this operation, consistent with the view that implicit processing does not rely on declarative memory mechanisms that engage the medial temporal lobe. In the context of recent FMRI findings, we raise the question whether Broca's region (or subregions) is specifically related to syntactic movement operations or the processing of hierarchically nested non-adjacent dependencies in the discussion section. We conclude that this is not the case. Instead, we argue that the left inferior frontal region is a generic on-line sequence processor that unifies information from various sources in an incremental and recursive manner, independent of whether there are any processing requirements related to syntactic movement or hierarchically nested structures. In addition, we argue that the Chomsky hierarchy is not directly relevant for neurobiological systems. (Contains 2 tables and 5 figures.)