On Invariant Synthesis for Parametric Systems

We study possibilities for automated invariant generation in parametric systems. We use (a refinement of) an algorithm for symbol elimination in theory extensions to devise a method for iteratively strengthening certain classes of safety properties to obtain invariants of the system. We identify conditions under which the method is correct and complete, and situations in which the method is guaranteed to terminate. We illustrate the ideas on various examples.Comment: 33 page

Combined Covers and Beth Definability (Extended Version)

In ESOP 2008, Gulwani and Musuvathi introduced a notion of cover and exploited it to handle infinite-state model checking problems. Motivated by applications to the verification of data-aware processes, we proved in a previous paper that covers are strictly related to model completions, a well-known topic in model theory. In this paper we investigate cover transfer to theory combinations in the disjoint signatures case. We prove that for convex theories, cover algorithms can be transferred to theory combinations under the same hypothesis (equality interpolation property aka strong amalgamation property) needed to transfer quantifier-free interpolation. In the non-convex case, we show by a counterexample that covers may not exist in the combined theories, even in case combined quantifier-free interpolants do exist. However, we exhibit a cover transfer algorithm operating also in the non-convex case for special kinds of theory combinations; these combinations (called `tame combinations') concern multi-sorted theories arising in many model-checking applications (in particular, the ones oriented to verification of data-aware processes)

Symbol Elimination for Parametric Second-Order Entailment Problems (with Applications to Problems in Wireless Network Theory)

We analyze possibilities of second-order quantifier elimination for formulae containing parameters -- constants or functions. For this, we use a constraint resolution calculus obtained from specializing the hierarchical superposition calculus. If saturation terminates, we analyze possibilities of obtaining weakest constraints on parameters which guarantee satisfiability. If the saturation does not terminate, we identify situations in which finite representations of infinite saturated sets exist. We identify situations in which entailment between formulae expressed using second-order quantification can be effectively checked. We illustrate the ideas on a series of examples from wireless network research.Comment: 44 page

Parametric Systems: Verification and Synthesis

In this paper we study possibilities of using hierarchical reasoning, symbol elimination and model generation for the verification of parametric systems, where the parameters can be constants or functions. Our goal is to automatically provide guarantees that such systems satisfy certain safety or invariance conditions. We analyze the possibility of automatically generating such guarantees in the form of constraints on parameters. We illustrate our methods on several examplesComment: 39 page

Automated Deduction – CADE 27 [electronic resource] : 27th International Conference on Automated Deduction, Natal, Brazil, August 27–30, 2019, Proceedings /

This book constitutes the proceeding of the 27th International Conference on Automated Deduction, CADE 27, held in Natal, Brazil, in August 2019. The 27 full papers and 7 system descriptions presented were carefully reviewed and selected from 65 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. .Automated Reasoning for Security Protocols -- Computer Deduction and (Formal) Proofs in Mathematics -- From Counter-Model-based Quantifier Instantiation to Quantifier Elimination in SMT -- The CADE-27 ATP System Competition - CASC-27 -- Unification modulo Lists with Reverse - Relation with Certain Word Equations -- On the Width of Regular Classes of Finite Structures -- Extending SMT solvers to Higher-Order Logic -- Superposition with Lambdas -- Restricted Combinatory Unification -- dLi: Definite Descriptions in Differential Dynamic Logic -- SPASS-SATT { A CDCL(LA) Solver -- GRUNGE: A Grand Unified ATP Challenge -- Model Completeness, Covers and Superposition -- A Tableaux Calculus for Default Intuitionistic Logic -- NIL: Learning Nonlinear Interpolants -- ENIGMA-NG: Efficient Neural and Gradient-Boosted Inference Guidance for E -- Towards Physical Hybrid Systems -- SCL -- Clause Learning from Simple Models -- Names are not just Sound and Smoke: Word Embeddings for Axiom Selection -- Computing Expected Runtimes for Constant Probability Programs -- Automatic Generation of Logical Models with AGES -- Automata Terms in a Lazy WSkS Decision Procedure -- Confluence by Critical Pair Analysis Revisited -- Composing Proof Terms -- Combining ProVerif and Automated Theorem Provers for Security Protocol Verification -- Towards Bit-Width-Independent Proofs in SMT Solvers -- On Invariant Synthesis for Parametric Systems -- The Aspect Calculus -- Uniform Substitution At One Fell Swoop -- A Formally Verified Abstract Account of Gödel's Incompleteness Theorems -- Old or Heavy? Decaying Gracefully with Age/Weight Shapes -- Induction in Saturation-Based Proof Search -- Faster, Higher, Stronger: E 2.3 -- Certified Equational Reasoning via Ordered Completion -- JGXYZ - An ATP System for Gap and Glut Logics -- GKC: a Reasoning System for Large Knowledge Bases -- Optimization Modulo the Theory of Floating-Point Numbers -- FAME(Q): An Automated Tool for Forgetting in Description Logics with Qualified Number Restrictions. .This book constitutes the proceeding of the 27th International Conference on Automated Deduction, CADE 27, held in Natal, Brazil, in August 2019. The 27 full papers and 7 system descriptions presented were carefully reviewed and selected from 65 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience.