SMT Solving for Functional Programming over Infinite Structures

SMT Solving for Functional Programming over Infinite Structures

We develop a simple functional programming language aimed at manipulating infinite, but first-order definable structures, such as the countably infinite clique graph or the set of all intervals with rational endpoints. Internally, such sets are represented by logical formulas that define them, and an external satisfiability modulo theories (SMT) solver is regularly run by the interpreter to che...

Programming Infinite Structures by Observations

Inductive datatypes provide mechanisms to define finite data such as finite lists and trees via constructors and allow programmers to analyze and manipulate finite data via pattern matching. In this paper, we develop a dual approach for working with infinite data structures such as streams. Infinite data inhabits coinductive datatypes which denote greatest fixpoints. Unlike finite data which is...

Virtual Substitution for SMT-Solving

SMT-solving aims at deciding satisfiability for the existential fragment of a first-order theory. A SAT-solver handles the logical part of a given problem and invokes an embedded theory solver to check consistency of theory constraints. For efficiency, the theory solver should be able to work incrementally and generate infeasible subsets. Currently available decision procedures for real algebra...

A new solving approach for fuzzy multi-objective programming problem in uncertainty conditions by ‎using semi-infinite linear programing

In practice, there are many problems which decision parameters are fuzzy numbers, and some kind of this problems are formulated as either possibilitic programming or multi-objective programming methods. In this paper, we consider a multi-objective programming problem with fuzzy data in constraints and introduce a new approach for solving these problems base on a combination of the multi-objecti...

Decision Problems for Finite Automata over Infinite Algebraic Structures