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Most modern (classical) programming languages support recursion. Recursion has also been successfully applied to the design of several quantum algorithms and introduced in a couple of quantum programming languages. So, it can be expected…
Boyer and Moore have discussed a recursive function that puts conditional expressions into normal form [1]. It is difficult to prove that this function terminates on all inputs. Three termination proofs are compared: (1) using a measure…
We consider linear recurrences with polynomial coefficients of Poincar\'e type and with a unique simple dominant eigenvalue. We give an algorithm that proves or disproves positivity of solutions provided the initial conditions satisfy a…
We present a unified deductive verification framework for first-order temporal properties based on well-founded rankings, where verification conditions are discharged using SMT solvers. To that end, we introduce a novel reduction from…
We present a series of definitions and theorems demonstrating how to reduce the requirements for proving system refinements ensuring containment of fair stuttering runs. A primary result of the work is the ability to reduce the requisite…
Our recently proposed certification framework for bit-level k-induction-based model checking has been shown to be quite effective in increasing the trust of verification results even though it partially involved quantifier reasoning. In…
While the standard formulation of quantum theory assumes a fixed background causal structure, one can relax this assumption within the so-called process matrix framework. Remarkably, some processes, termed causally nonseparable, are…
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…
A proof tableau of Hoare logic is an annotated program with pre- and post-conditions, which corresponds to an inference tree of Hoare logic. In this paper, we show that a proof tableau for partial correctness can be transformed into an…
We consider formal verification of recursive programs with resource consumption. We introduce prefix replacement systems with non-negative integer counters which can be incremented and reset to zero as a formal model for such programs. In…
Bounded verification has proved useful to detect bugs and to increase confidence in the correctness of a program. In contrast to unbounded verification, reasoning about calls via (bounded) inlining and about loops via (bounded) unrolling…
We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values),…
This paper develops a sign-separated finite-time error analysis for constant step-size Q-learning. Starting from the switching-system representation, the error is decomposed into its componentwise negative and positive parts. The negative…
In this paper we consider the problem of proving properties of infinite behaviour of formalisms suitable to describe (infinite state) systems with recursion and parallelism. As a formal setting, we consider the framework of Process…
A central task in quantum information science is state certification: testing whether an unknown state is $\epsilon_1$-close to a fixed target state, or $\epsilon_2$-far. Recent work has shown that surprisingly simple measurement…
Existing neural network verifiers compute a proof that each input is handled correctly under a given perturbation by propagating a symbolic abstraction of reachable values at each layer. This process is repeated from scratch independently…
Entangled quantum states are essential ingredients for many quantum technologies, but they must be validated before they are used. As a full characterization is prohibitively resource-intensive, recent work has focused on developing methods…
There is a large amount of work dedicated to the formal verification of security protocols. In this paper, we revisit and extend the NP-complete decision procedure for a bounded number of sessions. We use a, now standard, deducibility…
First-order logic has been established as an important tool for modeling and verifying intricate systems such as distributed protocols and concurrent systems. These systems are parametric in the number of nodes in the network or the number…
We consider quantum dynamical systems specified by a unitary operator U and an initial state vector \phi. In each step the unitary is followed by a projective measurement checking whether the system has returned to the initial state. We…