Abstract
The paper solves the main open problem of [BFG94]. We show that given two dependence alphabets (σ, D) and (σ′, D′), it is decidable whether there exists a strong coding h: M(σ, D)→M(σ′, D′) between the associated trace monoids. In fact, we show that the problem is NP-complete. (A coding is an injective homomorphism, it is strong if independent letters are mapped to independent traces.) We exhibit an example of trace monoids where a coding between them exists, but no strong coding. The decidability of codings remains open, in general. We have a lower and an upper bound, which show both to be strict. We further discuss encodings of free products of trace monoids and give almost optimal constructions.
In the final section, we state that the coding property is undecidable in a naturally arising class of homomorphisms.
This research has been supported by the ESPRIT Basic Research Action No. 6317 ASMICS 2, Algebraic and Syntactic Methods In Computer Science.
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Diekert, V., Muscholl, A., Reinhardt, K. (1995). On codings of traces. In: Mayr, E.W., Puech, C. (eds) STACS 95. STACS 1995. Lecture Notes in Computer Science, vol 900. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59042-0_90
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DOI: https://doi.org/10.1007/3-540-59042-0_90
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