Related papers: Certified Finite-State Induction for a Perturbed H…
We investigate here a new version of the Calculus of Inductive Constructions (CIC) on which the proof assistant Coq is based: the Calculus of Congruent Inductive Constructions, which truly extends CIC by building in arbitrary first-order…
The stabilization of a quantum computer by repeated error correction can be reduced almost entirely to repeated preparation of blocks of qubits in quantum codeword states. These are multi-particle entangled states with a high degree of…
With today's quantum processors venturing into regimes beyond the capabilities of classical devices [1-3], we face the challenge to verify that these devices perform as intended, even when we cannot check their results on classical…
This paper concerns state-based systems that interact with their environment at physically distributed interfaces, called ports. When such a system is used a projection of the global trace, called a local trace, is observed at each port.…
We address the problem of analyzing asynchronous event-driven programs, in which concurrent agents communicate via unbounded message queues. The safety verification problem for such programs is undecidable. We present in this paper a…
Deciding termination is a fundamental problem in the analysis of probabilistic imperative programs. We consider the qualitative and quantitative probabilistic termination problems for an imperative programming model with discrete…
Can one certify the preparation of a coherent, many-body quantum state by measurements with bounded accuracy in the presence of noise and decoherence? Here, we introduce a criterion to assess the fragility of large-scale quantum states…
Completion is one of the most studied techniques in term rewriting and fundamental to automated reasoning with equalities. In this paper we present new correctness proofs of abstract completion, both for finite and infinite runs. For the…
We prove, for stably computably enumerable formal systems, direct analogues of the first and second incompleteness theorems of G\"odel. A typical stably computably enumerable set is the set of Diophantine equations with no integer…
We study the implementability problem for an expressive class of symbolic communication protocols involving multiple participants. Our symbolic protocols describe infinite states and data values using dependent refinement predicates.…
We study safety verification for multithreaded programs with recursive parallelism (i.e. unbounded thread creation and recursion) as well as unbounded integer variables. Since the threads in each program configuration are structured in a…
I propose and investigate the use of continuous functional equations for the study of meta-Fibonacci integer sequences. This exploratory study includes three sequences with quite different behavior: Conway's famous sequence $A(n)=…
In this note we give a wellfoundedness proof of a computable notation system for first-order reflection.
SMT-based program analysis and verification often involve reasoning about program features that have been specified using quantifiers; incorporating quantifiers into SMT-based reasoning is, however, known to be challenging. If quantifier…
We define the problem identity check: Given a classical description of a quantum circuit, determine whether it is almost equivalent to the identity. Explicitly, the task is to decide whether the corresponding unitary is close to a complex…
Proof certificates can be used to validate the correctness of algebraic derivations. However, in practice, we frequently observed that the exact same proof steps are repeated for different sets of variables, which leads to unnecessarily…
Informal arguments that cryptographic protocols are secure can be made rigorous using inductive definitions. The approach is based on ordinary predicate calculus and copes with infinite-state systems. Proofs are generated using…
Probabilistic pushdown automata (pPDA) are a natural operational model for a variety of recursive discrete stochastic processes. In this paper, we study certificates - succinct and easily verifiable proofs - for upper and lower bounds on…
We revisit two well-established verification techniques, $k$-induction and bounded model checking (BMC), in the more general setting of fixed point theory over complete lattices. Our main theoretical contribution is latticed $k$-induction,…
Verification of quantum computations is crucial as experiments advance toward fault-tolerant quantum computing. Yet, no efficient protocol exists for certifying states generated in the Magic-State Injection model -- the foundation of…