Tradeoffs in Canonical Sequential Function Representations

State space exploration is of prime importance in the study of finite state sequential systems, with several efforts aimed at compact representation of the state space in order to tackle the state explosion problem. In our work with formal verification of inductively-defined hardware, we have identified a useful class of Boolean functions called Linearly Inductive Functions (LIFs). In this paper we explore the relationship between our LIF representation and the classic DFA (deterministic finite state automaton) representation of a sequential function, and examine the associated tradeoffs. We show that our LIF representation corresponds to a minimal reverse DFA, i.e. a minimal DFA which accepts the language consisting of the reverse input strings, where our implicit method for obtaining an LIF representation does not require explicit construction of a forward DFA. Its practical usefulness arises from our demonstration that reverse DFAs for several datapath circuits are exponentially more compact than the classic forward DFAs. Furthermore, in comparison to the traditional representation of DFAs as state transition diagrams, our LIF representations allow for state-sharing while maintainingdecomposition, resulting in memory savings in practice.