A Halting Algorithm to Determine the Existence of the Decoder

Automatic Decoder Synthesis: Methods and Case Studies

“…The experiments were conducted on a Linux machine with Xeon 2.53GHz CPU and 48GB RAM. The benchmark circuits and executable codes of prior work [20], [21] were obtained online [8]. The benchmark circuits and their statistics (including gate counts, circuit levels, register counts, and datapath widths) are listed in Table II.…”

“…We conducted three sets of experiments: comparison with [20] on decoder generation in Table III, comparison with [21] on decoder existence checking and generation in Table IV, and comparison with [21] on decoder existence checking for circuits without decoders in of [20], [21] were implemented in OCaml running zChaff [14], whereas ours were implemented in C running MiniSat [6]. The reported runtimes in [20] and [21] were obtained on a CentOS 5.2 Linux machine with AMD Athlon 64 X2 dual core 2.4GHz CPU and 6GB RAM, and with Intel Core 2 Q6600 2.4GHz CPU and 8GB RAM, respectively.…”

“…Recently Shen et al [20], [21] studied the decoder synthesis problem. A bounded decoder existence checking method was proposed [20], where the checking is with respect to a pre-specified parameter on observable output windows.…”

“…The necessity of pre-specifying the checking bound prevents decoder synthesis from being a fully automatic process. A later attempt [21] got one step closer to unbounded decoder existence checking. Despite its soundness, the proposed checking is unfortunately incomplete.…”

“…Figure 1 shows one such example, where a decoder does not exist, but the checking fails to decide. The problem results from the misconception that the notion of unique states [21] exactly captures the essence of decoder existence. However, there are state transition systems that consist of purely unique states and yet have no decoder as the example of Figure 1 suggests.…”