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Exotic Semi-Ring Constraints

10 pagesPublished: August 19, 2013


Exotic semi-ring constraints arise in a variety of applications and
in particular in the context of automated termination analysis.

We propose two techniques to solve such constraints: (a) to model
them using Boolean functions and integer linear arithmetic and solve
them using an SMT solver (QF_LIA, in certain cases also QF_IDL);
and (b) to seek finite domain solutions by applying unary bit-blasting
and solve them using a SAT solver.

In this note, we show the structure of such systems of constraints,
and report on the performance of SMT solvers and SAT encodings when
solving them. In particular, we observe that good results are
obtained by unary bit-blasting, improving on previous proposals to
apply binary bit-blasting. Moreover, our results indicate that, for
our benchmarks, unary bit-blasting leads to better results than the
ones directly obtained by an SMT solver.

Keyphrases: exotic semi-rings, order encoding, SAT encodings, SMT-IDL, SMT-LIA

In: Pascal Fontaine and Amit Goel (editors). SMT 2012. 10th International Workshop on Satisfiability Modulo Theories, vol 20, pages 88--97

BibTeX entry
  author    = {Michael Codish and Yoav Fekete and Carsten Fuhs and J\textbackslash{}"urgen Giesl and Johannes Waldmann},
  title     = {Exotic Semi-Ring Constraints},
  booktitle = {SMT 2012. 10th International Workshop on Satisfiability Modulo Theories},
  editor    = {Pascal Fontaine and Amit Goel},
  series    = {EPiC Series in Computing},
  volume    = {20},
  pages     = {88--97},
  year      = {2013},
  publisher = {EasyChair},
  bibsource = {EasyChair,},
  issn      = {2398-7340},
  url       = {},
  doi       = {10.29007/qqvt}}
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