Related papers: Uniformity within Parameterized Circuit Classes
Distinguishability takes a crucial rule in studying observability of hybrid system such as switched system. Recently, for two linear systems, Lou and Si gave a condition not only necessary but also sufficient to the distinguishability of…
We survey some results on the automatic verification of parameterized programs without identities. These are systems composed of arbitrarily many components, all of them running exactly the same finite-state program. We discuss the…
We refine the complexity landscape for enumeration problems by introducing very low classes defined by using Boolean circuits as enumerators. We locate well-known enumeration problems, e.g., from graph theory, Gray code enumeration, and…
In this article, we study parameterized complexity theory from the perspective of logic, or more specifically, descriptive complexity theory. We propose to consider parameterized model-checking problems for various fragments of first-order…
Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…
Although they differ in the functionality they offer, low-level systems exhibit certain patterns of design and utilization of computing resources. In this paper, we argue the position that modalities, in the sense of modal logic, should be…
We present the first fully automatic framework for verifying relational properties of parameterized quantum programs, i.e., a program that, given an input size, generates a corresponding quantum circuit. We focus on verifying input-output…
Monotone Boolean functions, and the monotone Boolean circuits that compute them, have been intensively studied in complexity theory. In this paper we study the structure of Boolean functions in terms of the minimum number of negations in…
Quantum Parametric Circuits are constructed as an alternative to reduce the size of quantum circuits, meaning to decrease the number of quantum gates and, consequently, the depth of these circuits. However, determining the optimal circuit…
Among the approximation methods for the verification of counter systems, one of them consists in model-checking their flat unfoldings. Unfortunately, the complexity characterization of model-checking problems for such operational models is…
Commutativity has proven to be a powerful tool in reasoning about concurrent programs. Recent work has shown that a commutativity-based reduction of a program may admit simpler proofs than the program itself. The framework of…
With the increased use of machine learning systems for decision making, questions about the fairness properties of such systems start to take center stage. Most existing work on algorithmic fairness assume complete observation of features…
We show that time complexity analysis of higher-order functional programs can be effectively reduced to an arguably simpler (although computationally equivalent) verification problem, namely checking first-order inequalities for validity.…
In the consistent histories formalism one specifies a family of histories as an exhaustive set of pairwise exclusive descriptions of the dynamics of a quantum system. We define branching families of histories, which strike a middle ground…
The circuit equivalence problem of a finite algebra $\mathbf A$ is the computational problem of deciding whether two circuits over $\mathbf A$ define the same function or not. This problem not just generalises the equivalence problem for…
In this paper, we consider bounded width circuits and nondeterministic circuits in three somewhat new directions. In the first part of this paper, we mainly consider bounded width circuits. The main purpose of this part is to prove that…
We establish a family of parametric isoperimetric-type inequalities with multiple geometric quantities for closed convex curves. These inequalities hold under certain parameter conditions. We also prove the equality conditions. Some new…
Equivalence checking of quantum circuits is an essential element in quantum program compilation, in which a quantum program can be synthesized into different quantum circuits that may vary in the number of qubits, initialization…
In this study, we analyze the Rademacher complexity $ \mathcal{R}_{M} $ of a parameterized unitary whose generators are chosen from $ n $-qubit Pauli strings. Although generalization bounds for quantum machine learning models have been…
Parametrised quantum circuits are a central framework for near term quantum machine learning. However, it remains challenging to determine in advance how architectural choices, such as encoding strategies, gate placement, and entangling…