Deep packet inspection is a fundamental task to improve network security and provide application-specific services. State-of-the-art systems adopt regular expressions due to their high expressive power. They are typically matched through deterministic finite automata (DFAs), but large rule sets need a memory amount that turns out to be too large for practical implementation. Many recent works have proposed improvements to address this issue, but they increase the number of transitions (and then of memory accesses) per character. This paper presents a new representation for DFAs, orthogonal to most of the previous solutions, called delta finite automata ( $\delta$FA), which considerably reduces states and transitions while preserving a transition per character only, thus allowing fast matching. A further optimization exploits $N$th order relationships within the DFA by adopting the concept of “temporary transitions.”