The influence of domain interpretations on computational models

Udi Boker*, Nachum Dershowitz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Computational models are usually defined over specific domains. For example, Turing machines are defined over strings, and the recursive functions over the natural numbers. Nevertheless, one often uses one computational model to compute functions over another domain, in which case, one is obliged to employ a representation, mapping elements of one domain into the other. For instance, Turing machines (or modern computers) are understood as computing numerical functions, by interpreting strings as numbers, via a binary or decimal representation, say. We ask: Is the choice of the domain interpretation important? Clearly, complexity is influenced, but does the representation also affect computability? Can it be that the same model computes strictly more functions via one representation than another? We show that the answer is "yes", and further analyze the influence of domain interpretation on the extensionality of computational models (that is, on the set of functions computed by the model). We introduce the notion of interpretation-completeness for computational models that are basically unaffected by the choice of domain interpretation, and prove that Turing machines and the recursive functions are interpretation-complete, while two-counter machines are incomplete. We continue by examining issues based on model extensionality that are influenced by the domain interpretation. We suggest a notion for comparing computational power of models operating over arbitrary domains, as well as an interpretation of the Church-Turing Thesis over arbitrary domains.

Original languageEnglish
Pages (from-to)1323-1339
Number of pages17
JournalApplied Mathematics and Computation
Issue number4
StatePublished - 15 Oct 2009


  • Computability
  • Computational comparison
  • Computational models
  • Computational power
  • Domain interpretation
  • Domain representation
  • Hypercomputation
  • Turing machine


Dive into the research topics of 'The influence of domain interpretations on computational models'. Together they form a unique fingerprint.

Cite this