Related papers: A Formalization of Polytime Functions
Over extended systems of finite type arithmetic, we utilize a formal representation of the outer measure to define a translation which allows for the systematic formalization of probabilistic statements. As a main result, this translation…
In this paper, we introduce new classes of functions that extend the known classes of functions of complex variable, such as entire functions, meromorphic functions, rational functions and polynomial functions and take values in the set of…
It is undecidable in general whether a given finitely presented group is word hyperbolic. We use the concept of pregroups, introduced by Stallings, to define a new class of van Kampen diagrams, which represent groups as quotients of…
We describe the formalisation in Coq of a proof that the numbers e and $\pi$ are transcendental. This proof lies at the interface of two domains of mathematics that are often considered separately: calculus (real and elementary complex…
In the past four decades, the notion of quantum polynomial-time computability has been mathematically modeled by quantum Turing machines as well as quantum circuits. This paper seeks the third model, which is a quantum analogue of the…
Many automatic theorem provers are restricted to untyped logics, and existing translations from typed logics are bulky or unsound. Recent research proposes monotonicity as a means to remove some clutter when translating monomorphic to…
This paper studies the class of logarithmically completely monotonic (LCM) functions. These functions play an important role in characterising externally positive linear systems which find applications in important control problems such as…
Polyregular functions are the class of string-to-string functions definable by pebble transducers, an extension of finite-state automata with outputs and multiple two-way reading heads (pebbles) with a stack discipline. If a polyregular…
The use of formal methods provides confidence in the correctness of developments. Yet one may argue about the actual level of confidence obtained when the method itself -- or its implementation -- is not formally checked. We address this…
The main purpose of this work is to prove characterization theorems for generalized moment functions on groups. According one of the main results these are exponential polynomials that can be described with the aid of complete (exponential)…
The constant-time discipline is a software-based countermeasure used for protecting high assurance cryptographic implementations against timing side-channel attacks. Constant-time is effective (it protects against many known attacks),…
The sumcheck protocol, introduced in 1992, is an interactive proof which is a key component of many probabilistic proof systems in computational complexity theory and cryptography, some of which have been deployed. However, none of these…
In this paper we show that if an entire function $f(z_1,z_2)$ of two (or more) complex variables verifies $\norm{f(z_1,z_2)}\leq K(\norm{P(z_1,z_2)})$, where $P(z_1,z_2)$ is a polynomial that is not a power in $\CC[[z_1,z_2]]$, and $K$ is…
Polymorphic variants are a useful feature of the OCaml language whose current definition and implementation rely on kinding constraints to simulate a subtyping relation via unification. This yields an awkward formalization and results in a…
In this article we present a method to implement orthogonal polynomials and many other special functions in Computer Algebra systems enabling the user to work with those functions appropriately, and in particular to verify different types…
We study when partial Boolean functions can (and cannot) exhibit superpolynomial quantum query speedups, and develop a general framework for ruling out such speedups via two complementary lenses: promise-aware complexity measures and…
We study the classical problem of verifying programs with respect to formal specifications given in the linear temporal logic (LTL). We first present novel sound and complete witnesses for LTL verification over imperative programs. Our…
We give a direct and elementary proof of the theorem on formal functions by studying the behaviour of the Godement resolution of a sheaf of modules under completion.
We give a characterization of deterministic polynomial time computation based on an algebraic structure called the resolution semiring, whose elements can be understood as logic programs or sets of rewriting rules over first-order terms.…
We initiate the study of the cohomology of (strict polynomial) bifunctors by introducing the foundational formalism, establishing numerous properties in analogy with the cohomology of functors, and providing computational techniques. Since…