Related papers: Certified Finite-State Induction for a Perturbed H…
In this paper we study a generalized model named one-way general quantum finite automata} (1gQFA), in which each symbol in the input alphabet induces a trace-preserving quantum operation, instead of a unitary transformation. Two different…
Quantitative logic reasons about the degree to which formulas are satisfied. This paper studies the fundamental reasoning principles of higher-order quantitative logic and their application to reasoning about probabilistic programs and…
Infinite-state systems such as distributed protocols are challenging to verify using interactive theorem provers or automatic verification tools. Of these techniques, deductive verification is highly expressive but requires the user to…
This paper aims at carrying out termination proofs for simply typed higher-order calculi automatically by using ordering comparisons. To this end, we introduce the computability path ordering (CPO), a recursive relation on terms obtained by…
Termination is an important property of programs; notably required for programs formulated in proof assistants. It is a very active subject of research in the Turing-complete formalism of term rewriting systems, where many methods and tools…
Quantum state verification plays a vital role in many quantum cryptographic protocols, as it allows the use of quantum states from untrusted sources. While some progress has been made in this direction, the question of whether the most…
For $p, q\in \mathbb{N}$, a finite nonempty set $F$ is said to be $(p,q)$-Schreier (or maximal $(p,q)$-Schreier, respectively) if $q\min F\ge p|F|$ (or $q\min F = p|F|$, respectively). For $n\in \mathbb{N}$, let $$\mathcal{S}^{p/q}_{n}\ :=\…
QNNVerifier is the first open-source tool for verifying implementations of neural networks that takes into account the finite word-length (i.e. quantization) of their operands. The novel support for quantization is achieved by employing…
Designing quantum processors is a complex task that demands advanced verification methods to ensure their correct functionality. However, traditional methods of comprehensively verifying quantum devices, such as quantum process tomography,…
We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
Parameterized systems play a crucial role in the computer field, and their security is of great significance. Formal verification of parameterized protocols is especially challenging due to its "parameterized" feature, which brings…
Despite recent advances in automating theorem proving in full first-order theories, inductive reasoning still poses a serious challenge to state-of-the-art theorem provers. The reason for that is that in first-order logic induction requires…
We show that any number of parties can coherently exchange any one pure quantum state for another, without communication, given prior shared entanglement. Two applications of this fact to the study of multi-prover quantum interactive proof…
Model checking properties are often described by means of finite automata. Any particular such automaton divides the set of infinite trees into finitely many classes, according to which state has an infinite run. Building the full type…
Modern machine learning models are sensitive to the manipulation of both the training data (poisoning attacks) and inference data (adversarial examples). Recognizing this issue, the community has developed many empirical defenses against…
Despite recent advances in automating theorem proving in full first-order theories, inductive reasoning still poses a serious challenge to state-of-the-art theorem provers. The reason for that is that in first-order logic induction requires…
Computational security in cryptography has a risk that computational assumptions underlying the security are broken in the future. One solution is to construct information-theoretically-secure protocols, but many cryptographic primitives…
Interactive verification protocols for quantum computations allow to build trust between a client and a service provider, ensuring the former that the instructed computation was carried out faithfully. They come in two variants, one without…
We study parity features as representations that can be evaluated entirely classically once the binary or quantized input representation and parity words are fixed, particularly when labels depend on higher-order feature interactions or…