Related papers: Implicit Real Vector Automata
Symbolic regression is a type of discrete optimization problem that involves searching expressions that fit given data points. In many cases, other mathematical constraints about the unknown expression not only provide more information…
Continuing a well established tradition of associating convex bodies to monomial ideals, we initiate a program to construct asymptotic Newton polyhedra from decompositions of monomial ideals. This is achieved by forming a graded family of…
We introduce first order alternating automata, a generalization of boolean alternating automata, in which transition rules are described by multisorted first order formulae, with states and internal variables given by uninterpreted…
We show that one can enumerate the vertices of the convex hull of integer points in polytopes whose constraint matrices have bounded and nonzero subdeterminants, in time polynomial in the dimension and encoding size of the polytope. This…
We consider the problem of image representation for the tasks of unsupervised learning and semi-supervised learning. In those learning tasks, the raw image vectors may not provide enough representation for their intrinsic structures due to…
In this paper we give an Immerman's Theorem for real-valued computation. We define circuits operating over real numbers and show that families of such circuits of polynomial size and constant depth decide exactly those sets of vectors of…
A computationally efficient reformulation of the rigid tube model predictive control is developed. A unique feature of the derived formulation is the utilization of the implicit set representations. This novel formulation does not require…
Transformer-based language models often achieve strong results on mathematical reasoning benchmarks while remaining fragile on basic numerical understanding and arithmetic operations. A central limitation is that numbers are processed as…
Although models are built on the basis of some observations of reality, the concepts that derive theoretically from their definitions as well as from their characteristics and properties are not necessarily direct consequences of these…
We use the implicitization procedure to generate polynomial equality constraints on the set of distributions induced by local interventions on variables governed by a causal Bayesian network with hidden variables. We show how we may reduce…
Many constraints restricting the result of some computations over an integer sequence can be compactly represented by register automata. We improve the propagation of the conjunction of such constraints on the same sequence by synthesising…
We suggest a programming realization of an algorithm for verifying a given set of algebraic relations in the form of a supercommutator multiplication table for the Verma module, which is constructed according to a generalized Cartan…
To simplify the analysis of Boolean networks, a reduction in the number of components is often considered. A popular reduction method consists in eliminating components that are not autoregulated, using variable substitution. In this work,…
We exhibit an algorithm to compute the strongest algebraic (or polynomial) invariants that hold at each location of a given unguarded linear hybrid automaton (i.e., a hybrid automaton having only unguarded transitions, all of whose…
We introduce a certain restriction of weighted automata over the rationals, called image-binary automata. We show that such automata accept the regular languages, can be exponentially more succinct than corresponding NFAs, and allow for…
This survey paper is aimed to describe a relatively new branch of symbolic dynamics which we call Arithmetic Dynamics. It deals with explicit arithmetic expansions of reals and vectors that have a "dynamical" sense. This means precisely…
We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…
In this work, we introduce a new class of non-convex functions, called implicit concave functions, which are compositions of a concave function with a continuously differentiable mapping. We analyze the properties of their minimization by…
This paper addresses the problem of identifying parsimonious explicit piece-wise polynomial relationships that might involve a relatively large number of raw features. The algorithm leverages a recently proposed identification algorithm…
We revisit the complexity of procedures on SFAs (such as intersection, emptiness, etc.) and analyze them according to the measures we find suitable for symbolic automata: the number of states, the maximal number of transitions exiting a…