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The paper is devoted to the methods of solving simultaneous recurrences. Specifically, we discuss transformation of matrix recurrences to regular recurrences and propose a way of solving special matrix recurrences of order three by their…
Many problems in machine learning can be solved by rounding the solution of an appropriate linear program (LP). This paper shows that we can recover solutions of comparable quality by rounding an approximate LP solution instead of the ex-…
We are interested in solutions of a norm form equation that takes values in a given multi-recurrence. We show that among the solutions there are only finitely many values in each component which lie in the given multi-recurrence unless the…
The systematic approach to solving the recurrence relations for multi-loop integrals is described. In particular, the criteria of their reducibility is suggested.
One of the important tasks of the Reliability Estimation is Analysis of the Fault Tree. A problem of Fault Trees analysis is considered one of the most complex ones, since structure of such trees is characterized by a considerable number of…
Complex reasoning problems are most clearly and easily specified using logical rules, but require recursive rules with aggregation such as count and sum for practical applications. Unfortunately, the meaning of such rules has been a…
In most introductory numerical analysis textbooks, the treatment of a single nonlinear equation often consists of a collection of all-purpose methods that frequently do not work or are inefficient. These textbooks neglect to teach the…
Even if path planning can be solved using standard techniques from dynamic programming and control, the problem can also be approached using probabilistic inference. The algorithms that emerge using the latter framework bear some appealing…
Great advances in program analysis would be enabled if it were possible to derive the function of a program from inputs to outputs (or from initial states to final states, depending on how we model program semantics). Efforts to do so have…
Program synthesis is a class of regression problems where one seeks a solution, in the form of a source-code program, mapping the inputs to their corresponding outputs exactly. Due to its precise and combinatorial nature, program synthesis…
Pragmas for loop transformations, such as unrolling, are implemented in most mainstream compilers. They are used by application programmers because of their ease of use compared to directly modifying the source code of the relevant loops.…
We present a new method for inferring complexity properties for a class of programs in the form of flowcharts annotated with loop information. Specifically, our method can (soundly and completely) decide if computed values are polynomially…
In this paper we study the tightness of solutions for a family of recursion equations. These equations arise naturally in the study of random walks on tree-like structures. Examples include the maximal displacement of a branching random…
Runtime repeated recursion unfolding was recently introduced as a just-in-time program transformation strategy that can achieve super-linear speedup. So far, the method was restricted to single linear direct recursive rules in the…
We introduce a just-in-time runtime program transformation strategy based on repeated recursion unfolding. Our online program optimization generates several versions of a recursion differentiated by the minimal number of recursive steps…
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…
Path-following algorithms are frequently used in composite optimization problems where a series of subproblems, with varying regularization hyperparameters, are solved sequentially. By reusing the previous solutions as initialization,…
Repeated recursion unfolding is a new approach that repeatedly unfolds a recursion with itself and simplifies it while keeping all unfolded rules. Each unfolding doubles the number of recursive steps covered. This reduces the number of…
Fully automatic worst-case complexity analysis has a number of applications in computer-assisted program manipulation. A classical and powerful approach to complexity analysis consists in formally deriving, from the program syntax, a set of…
Cooperative constraint solving is an area of constraint programming that studies the interaction between constraint solvers with the aim of discovering the interaction patterns that amplify the positive qualities of individual solvers.…