Related papers: A Formalization of Polytime Functions
We introduce the notion of numerical functors to generalise Eilenberg & MacLane's polynomial functors to modules over a binomial base ring. After shewing how these functors are encoded by modules over a certain ring, we record a precise…
Two emergent properties in aggregation theory are investigated, namely horizontal maxitivity and comonotonic maxitivity (as well as their dual counterparts) which are commonly defined by means of certain functional equations. We completely…
Theory of choreographic languages typically includes a number of complex results that are proved by structural induction. The high number of cases and the subtle details in some of them lead to long reviewing processes, and occasionally to…
Within the framework of mappings between affine spaces, the notion of $n$-th polarization of a function will lead to an intrinsic characterization of polynomial functions. We prove that the characteristic features of derivations, such as…
We propose an extension of the framework for discussing the computational complexity of problems involving uncountably many objects, such as real numbers, sets and functions, that can be represented only through approximation. The key idea…
We give new proofs of soundness (all representable functions on base types lies in certain complexity classes) for Elementary Affine Logic, LFPL (a language for polytime computation close to realistic functional programming introduced by…
Interpretation methods and their restrictions to polynomials have been deeply used to control the termination and complexity of first-order term rewrite systems. This paper extends interpretation methods to a pure higher order functional…
Let $R$ be a finite commutative ring with $1\ne 0$. The set $\mathcal{F}(R)$ of polynomial functions on $R$ is a finite commutative ring with pointwise operations. Its group of units $\mathcal{F}(R)^\times$ is just the set of all…
Brief Description: The book provides a unique highly self-contained text introducing the reader to the classical and modern theory of polyanalytic functions and their generalizations. This is a subbranch of complex analysis of several…
A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be…
Developing secure distributed systems is difficult, and even harder when advanced cryptography must be used to achieve security goals. Following prior work, we advocate using secure program partitioning to synthesize cryptographic…
We introduce a new bounded theory RS^1_2 and show that the functions which are Sigma^b_1-representable in it are precisely random functions which can be computed in polynomial time. Concretely, we pass through a class of oracle functions…
We define formal geometric quantisation for proper Hamiltonian actions by possibly noncompact groups on possibly noncompact, prequantised symplectic manifolds, generalising work of Weitsman and Paradan. We study the functorial properties of…
We introduce a formal framework for analyzing trades in financial markets. These days, all big exchanges use computer algorithms to match buy and sell requests and these algorithms must abide by certain regulatory guidelines. For example,…
We give a new proof that bounded non-commutative functions on polynomial polyhedra can be represented by a realization formula, a generalization of the transfer function realization formula for bounded analytic functions on the unit disk.
We study the polyregular string-to-string functions, which are certain functions of polynomial output size that can be described using automata and logic. We describe a system of combinators that generates exactly these functions. Unlike…
We discuss various formalisms to describe string-to-string transformations. Many are based on automata and can be seen as operational descriptions, allowing direct implementations when the input scanner is deterministic. Alternatively, one…
This paper presents a logical approach to the translation of functional calculi into concurrent process calculi. The starting point is a type system for the {\pi}-calculus closely related to linear logic. Decompositions of intuitionistic…
Many potentially non-terminating functions cannot be directly defined in a logic of total functions, such as HOL. A well-known solution to this is to define non-terminating functions using a clock that forces termination at a certain depth…
In this paper some classes of local polynomial functions on abelian groups are characterized by the properties of their variety. For this characterization we introduce a numerical quantity depending on the variety of the local polynomial…