First-Order Transitive Closure Axiomatization via Iterative Invariant Injections

  • Aboubakr Achraf El GhaziEmail author
  • Mana Taghdiri
  • Mihai Herda
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9058)


This paper presents an approach for proving the validity of first-order relational formulas that involve transitive closure. Given a formula \(F\) that includes the transitive closure of a relation \(R\), our approach can deduce a complete (pure) first-order axiomatization of the paths of \(R\) that occur in \(F\). Such axiomatization enables full automated verification of \(F\) using an automatic theorem prover like Z3. This is done via an iterative detection and injection of \(R\)-invariants —invariant formulas with respect to \(R\)-transitions in the context of \(F\). This paper presents a proof for the correctness of the approach, and reports on its application to non-trivial Alloy benchmarks.


First-order relational logic Transitive closure Axiomatization Specification Verification Alloy SMT solving 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Aboubakr Achraf El Ghazi
    • 1
    Email author
  • Mana Taghdiri
    • 1
  • Mihai Herda
    • 1
  1. 1.Karlsruhe Institute of TechnologyKarlsruheGermany

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