Optimizing mkbTT

We describe performance enhancements that have been added to mkbTT, a modern completion tool combining multi-completion with the use of termination tools

Extensional Higher-Order Paramodulation in Leo-III

Leo-III is an automated theorem prover for extensional type theory with Henkin semantics and choice. Reasoning with primitive equality is enabled by adapting paramodulation-based proof search to higher-order logic. The prover may cooperate with multiple external specialist reasoning systems such as first-order provers and SMT solvers. Leo-III is compatible with the TPTP/TSTP framework for input formats, reporting results and proofs, and standardized communication between reasoning systems, enabling e.g. proof reconstruction from within proof assistants such as Isabelle/HOL. Leo-III supports reasoning in polymorphic first-order and higher-order logic, in all normal quantified modal logics, as well as in different deontic logics. Its development had initiated the ongoing extension of the TPTP infrastructure to reasoning within non-classical logics.Comment: 34 pages, 7 Figures, 1 Table; submitted articl

Automated Verification for Functional and Relational Properties of Voting Rules

In this paper, we formalise classes of axiomatic properties for voting rules, discuss their characteristics, and show how symmetry properties can be exploited in the verification of other properties. Following that, we describe how automated verification methods such as software bounded model checking and deductive verification can be used to verify implementations of voting rules. We present a case study, where we use and compare different approaches to verify that plurality voting satisfies the majority and the anonymity property

A Formally Verified Checker for First-Order Proofs

The Verified TESC Verifier (VTV) is a formally verified checker for the new Theory-Extensible Sequent Calculus (TESC) proof format for first-order ATPs. VTV accepts a TPTP problem and a TESC proof as input, and uses the latter to verify the unsatisfiability of the former. VTV is written in Agda, and the soundness of its proof-checking kernel is verified in respect to a first-order semantics formalized in Agda. VTV shows robust performance in a comprehensive test using all eligible problems from the TPTP problem library, successfully verifying all but the largest 5 of 12296 proofs, with >97% of the proofs verified in less than 1 second

Predicting Memory Demands of BDD Operations using Maximum Graph Cuts (Extended Paper)

The BDD package Adiar manipulates Binary Decision Diagrams (BDDs) in external memory. This enables handling big BDDs, but the performance suffers when dealing with moderate-sized BDDs. This is mostly due to initializing expensive external memory data structures, even if their contents can fit entirely inside internal memory. The contents of these auxiliary data structures always correspond to a graph cut in an input or output BDD. Specifically, these cuts respect the levels of the BDD. We formalise the shape of these cuts and prove sound upper bounds on their maximum size for each BDD operation. We have implemented these upper bounds within Adiar. With these bounds, it can predict whether a faster internal memory variant of the auxiliary data structures can be used. In practice, this improves Adiar's running time across the board. Specifically for the moderate-sized BDDs, this results in an average reduction of the computation time by 86.1% (median of 89.7%). In some cases, the difference is even 99.9\%. When checking equivalence of hardware circuits from the EPFL Benchmark Suite, for one of the instances the time was decreased by 52 hours.Comment: 25 pages, 11 Figures, 2 Tables. Extended version of paper published at ATVA 202