Rodrigo Otoni

We present PyCHC , a solver-agnostic framework aimed at systems of constrained Horn clauses (CHC). PyCHC provides intuitive Python APIs to create and manipulate CHC systems programmatically, and solve them using different backend solvers. Furthermore, PyCHC offers a certification pipeline to validate the correctness of results reported by the CHC solvers, via the use of independent satisfiability modulo theories (SMT) solvers and proof checkers. We present our framework’s architecture and features, and demonstrate how it enables rapid prototyping of new CHC-based algorithms and experimentation with novel strategies for cooperative solving. We used PyCHC to validate the results of the Eldarica , Golem , and Z3-Spacer solvers on CHC-COMP benchmarks, finding several issues across different tool versions.

This paper presents a novel iterative approach to achieve effective and efficient approximate logic synthesis (ALS). The core idea is to perform circuit rewriting in a way that is both local, i.e., is applied piece-wise to selected subcircuits, and extensive, i.e., systematically explores the design space for good solutions. Concretely, we propose SubXPAT, a new Boolean rewriting framework which iteratively employs satisfiability modulo theories (SMT) solving to select and approximate key parts of a circuit. Selection aims at finding subcircuits that at the same time include a significant number of gates and can be efficiently approximated, which is done by searching for large convex subcircuits with a limited number of inputs and outputs. Approximation is guided by the use of a parametric template, structured as a sum of products, which allows for fine-grained control over the subcircuit characteristics. SubXPAT was implemented as an open-source tool and compared against other ALS tools implementing state-of-the-art techniques. Our experimental evaluation used a broad range of arithmetic circuits with different bit-widths and our results indicate that SubXPAT generates approximate circuits that are more area-efficient than those generated by state-of-the-art techniques in 72% of the cases.

Formal verification tooling increasingly relies on logic solvers as automated reasoning engines. A commonality among these solvers is the high complexity of their codebases, which makes bug occurrence disturbingly frequent. Tool competitions have showcased many examples of state-of-the-art solvers disagreeing on the satisfiability of logic formulas, be it solvers for Boolean satisfiability (SAT), satisfiability modulo theories (SMT), or constrained Horn clauses (CHC). The validation of solvers’ results is thus of paramount importance, in order to increase the confidence not only in the solvers themselves but also in the tooling which they underpin. Among the formalisms commonly used by modern verification tools, CHC is one that has seen, at the same time, extensive practical usage and very little effort in result validation. We propose a two-layered validation approach for witnesses of CHC satisfiability that validates CHC models via proof-backed SMT queries. We developed a modular evaluation framework, ATHENA, and assessed the approach’s viability via large scale experimentation, comparing three CHC solvers, five SMT solvers, and five proof checkers. Our results indicate that the approach is feasible, with the potential to be incorporated into CHC-based tooling, and also confirm the need for validation, with fourteen bugs being found in the tools used.

Quantum networks have capabilities that are impossible to achieve using only classical information. They connect quantum capable nodes, with their fundamental unit of communication being the Bell pair , a pair of entangled quantum bits. Due to the nature of quantum phenomena, Bell pairs are fragile and difficult to transmit over long distances, thus requiring a network of repeaters along with dedicated hardware and software to ensure the desired results. The intrinsic challenges associated with quantum networks, such as competition over shared resources and high probabilities of failure, require quantitative reasoning about quantum network protocols. This paper develops PBKAT, an expressive language for specification, verification and optimization of quantum network protocols for Bell pair distribution. Our language is equipped with primitives for expressing probabilistic and possibilistic behaviors, and with semantics modeling protocol executions. We establish the properties of PBKAT’s semantics, which we use for quantitative analysis of protocol behavior. We further implement a tool to automate PBKAT’s usage, which we evaluated on real-world protocols drawn from the literature. Our results indicate that PBKAT is well suited for both expressing real-world quantum network protocols and reasoning about their quantitative properties.

Many verification tools currently rely on logic solvers as backend reasoning engines. Despite playing such a pivotal role, bugs are not uncommon in the complex codebases of these solvers. Validating their results is thus critical, with correctness witnesses often being used for this end. Output validation for constrained Horn clauses (CHC) solvers is not a well explored topic though, especially in regards to unsatisfiability results. This is a significant issue, given that CHC solvers are being increasingly employed in verification tooling. To address it, we propose an approach to validate CHC unsatisfiability results based on independently checkable proofs. Our approach is generic in regards to the solving algorithm, preprocessing steps, and exact proof format used, and works by first producing a coarse-grained proof during solving and then instantiating it into a suitable proof format by adding missing details, at which point the instantiated proof can be checked by an independent proof checker. We instrumented a state-of-the-art CHC solver to generate proofs in the Alethe format and performed a large-scale evaluation. Our results indicate that proofs can be produced with minimal overhead, can be efficiently checked, and have tractable sizes.

Quantum networks connect quantum capable nodes in order to achieve capabilities that are impossible only using classical information. Their fundamental unit of communication is the Bell pair , which consists of two entangled quantum bits. Unfortunately, Bell pairs are fragile and difficult to transmit directly, necessitating a network of repeaters, along with software and hardware that can ensure the desired results. Challenging intrinsic features of quantum networks, such as dealing with resource competition, motivate formal reasoning about quantum network protocols. To this end, we developed BellKAT, a novel specification language for quantum networks based upon Kleene algebra. To cater to the specific needs of quantum networks, we designed an algebraic structure, called BellSKA, which we use as the basis of BellKAT’s denotational semantics. BellKAT’s constructs describe entanglement distribution rules that allow for modular specification. We give BellKAT a sound and complete equational theory, allowing us to verify network protocols. We provide a prototype tool to showcase the expressiveness of BellKAT and how to optimize and verify networks in practice.