Related papers: Unique Solutions of Guarded Recursive Equations
The study of the recently constructed group foliation for the geopotential forecast equation is continued. The group foliation consists of two systems, namely the automorphic and resolving systems, the analysis of which facilitates the…
Runtime efficiency and termination are crucial properties in the studies of program verification. Instead of dealing with these issues in an ad hoc manner, it would be useful to develop a robust framework in which such properties are…
This paper describes a generalization of Clark's completion that is applicable to logic programs containing arithmetic operations and produces syntactically simple, natural looking formulas. If a set of first-order axioms is equivalent to…
Understanding the structural evolution of granular systems is a long-standing problem. A recently proposed theory for such dynamics in two dimensions predicts that steady states of very dense systems satisfy detailed-balance. We analyse…
In this paper, an optimal switching problem is proposed for one-dimensional reflected backward stochastic differential equations (RBSDEs, for short) where the generators, the terminal values and the barriers are all switched with positive…
Recursive blocked algorithms have proven to be highly efficient at the numerical solution of the Sylvester matrix equation and its generalizations. In this work, we show that these algorithms extend in a seamless fashion to…
The problem of determining whether a probabilistic program terminates almost surely (i.e.~with probability one) is undecidable, and actually $\Pi^0_2$-complete. For this reason, a growing literature has explored classes of programs for…
Recently, in order to mix algebraic and logic styles of specification in a uniform framework, the notion of a logic labelled transition system (Logic LTS or LLTS for short) has been introduced and explored. A variety of constructors over…
Reversible systems feature both forward computations and backward computations, where the latter undo the effects of the former in a causally consistent manner. The compositionality properties and equational characterizations of strong and…
In this paper, we study doubly reflected Backward Stochastic Differential Equations defined on probability spaces equipped with filtration satisfying only the usual assumptions of right continuity and completeness in the case where the…
Structural resolution (or S-resolution) is a newly proposed alternative to SLD-resolution that allows a systematic separation of derivations into term-matching and unification steps. Productive logic programs are those for which…
Solving a singular linear system for an individual vector solution is an ill-posed problem with a condition number infinity. From an alternative perspective, however, the general solution of a singular system is of a bounded sensitivity as…
We study the existence of singular separable solutions to a class of quasilinear equations with reaction term. In the 2-dim case, we use a dynamical system approach to construct our solutions.
Evaluating a Boolean conjunctive query Q against a guarded first-order theory F is equivalent to checking whether "F and not Q" is unsatisfiable. This problem is relevant to the areas of database theory and description logic. Since Q may…
Guarded Kleene Algebra with Tests (GKAT) is an efficient fragment of KAT, as it allows for almost linear decidability of equivalence. In this paper, we study the (co)algebraic properties of GKAT. Our initial focus is on the fragment that…
We establish a general existence and uniqueness of integrable adapted solutions to scalar backward stochastic differential equations with integrable parameters, where the generator $g$ has an iterated-logarithmic uniform continuity in the…
In this paper, we investigate the global conservative solutions to the generalized Camassa-Holm equation with dual-power nonlinearities. By introducing a new set of variables, we transform the original equation into an equivalent…
We present an expressive logic over trace formulas, based on binary state predicates, chop, and least fixed-points, for precise specification of programs with recursive procedures. Both, programs and trace formulas, are equipped with a…
In this work we prove uniqueness result for an implicit discrete system defined on connected graphs. Our discrete system is motivated from a certain class of spatial segregation of reaction-diffusion equations.
A single-index model (SIM) provides for parsimonious multi-dimensional nonlinear regression by combining parametric (linear) projection with univariate nonparametric (non-linear) regression models. We show that a particular Gaussian process…