Constraint Logic Programming Research Articles

Unifying Effectiveness and Efficiency in Sustainable Supply Chain Management in Automotive: the 21st EWA Edu Model Enhanced by Wholeness Systems Thinking for Lifelong Learning

The contemporary business environment is characterized by VUCA (volatility, uncertainty, complexity, ambiguity), influencing many industries, notably automotive. As humanity encounters the finite constraints of Earth's ecosystems, it becomes imperative for strategic management to transcend mere economic metrics and incorporate environmental and social dimensions. This paper explores the critical role of Wholeness Systems Thinking (WST) in transitioning from traditional Knowledge-based educational frameworks that emphasize a Maximization Mindset to those fostering an Understanding-based, Purposeful mindset in lifelong learning. Employing the sustainable educational model, 21st EWA Edu, this approach cultivates a human capital intellectual capability. Furthermore, the study investigates how this paradigm aids in harmonizing the concepts of effectiveness and efficiency within Sustainable Supply Chain Management (SSCM). The findings indicate that when applied to lifelong learning, this novel intellectual capacity not only refines decision-making processes but also ensures alignment between long-term sustainability objectives and short-term operational strategies in the automotive sector.

Combining Type Checking and Set Constraint Solving to Improve Automated Software Verification

Abstract This technical note shows how we have combined prescriptive type checking and constraint solving to increase automation during software verification. We do so by defining a type system and implementing a typechecker for $\{log\}$ (read ‘setlog’), a Constraint Logic Programming language and satisfiability solver based on set theory. The constraint solver is proved to be safe w.r.t. the type system. Two industrial-strength case studies are presented where this combination is used with very good results.

From Single-Objective to Bi-Objective Maximum Satisfiability Solving

The declarative approach is key to efficiently finding optimal solutions to various types of NP-hard real-world combinatorial optimization problems. Most work on practical declarative solvers—ranging from classical integer programming to finite-domain constraint optimization and maximum satisfiability (MaxSAT)—has focused on optimization under a single objective; fewer advances have been made towards efficient declarative techniques for multi-objective optimization problems. Motivated by significant recent advances in practical solvers for MaxSAT, in this work we develop BiOptSat, an exact declarative approach for finding Pareto-optimal solutions to bi-objective optimization problems, with propositional logic as the underlying constraint language. BiOptSat can be viewed as an instantiation of the lexicographic method. The approach makes use of a single Boolean satisfiability solver that is incrementally employed throughout the entire search procedure, allowing for finding a single Pareto-optimal solution, finding one representative solution for each non-dominated point, and enumerating all Pareto-optimal solutions. We detail several algorithmic instantiations of BiOptSat, each building on recent algorithms proposed for single-objective MaxSAT. We empirically evaluate the instantiations compared to recently-proposed alternative approaches to multi-objective MaxSAT solving on several real-world domains from the literature, showing the practical benefits of our approach.

Geometric reasoning on the euclidean traveling salesperson problem in answer set programming1

The Traveling Salesperson Problem (TSP) is one of the best-known problems in computer science. Many instances and real world applications fall into the Euclidean TSP special case, in which each node is identified by its coordinates on the plane and the Euclidean distance is used as cost function. It is worth noting that in the Euclidean TSP more information is available than in the general case; in a previous publication, the use of geometric information has been exploited to speedup TSP solving for Constraint Logic Programming (CLP) solvers. In this work, we study the applicability of geometric reasoning to the Euclidean TSP in the context of an ASP computation. We compare experimentally a classical ASP approach to the TSP and the effect of the reasoning based on geometric properties. We also compare the speedup of the additional filtering based on geometric information on an ASP solver and a CLP on Finite Domain (CLP(FD)) solver.

Optimal Polynomial-Time Compression for Boolean Max CSP

In the Boolean maximum constraint satisfaction problem— Max CSPΓ —one is given a collection of weighted applications of constraints from a finite constraint language Γ, over a common set of variables, and the goal is to assign Boolean values to the variables so that the total weight of satisfied constraints is maximized. There exists a concise dichotomy theorem providing a criterion on Γ for the problem to be polynomial-time solvable and stating that otherwise, it becomes NP-hard. We study the NP-hard cases through the lens of kernelization and provide a complete characterization of Max CSPΓ with respect to the optimal compression size. Namely, we prove that Max CSPΓ parameterized by the number of variables n is either polynomial-time solvable, or there exists an integer d ≥ 2 depending on Γ, such that: (1) An instance of Max CSPΓ can be compressed into an equivalent instance with 𝒪( n d log n ) bits in polynomial time, (2) Max CSPΓ does not admit such a compression to 𝒪( n d-ε ) bits unless NP ⊆ co-NP / poly. Our reductions are based on interpreting constraints as multilinear polynomials combined with the framework of “constraint implementations”, formerly used in the context of APX-hardness. As another application of our reductions, we reveal tight connections between optimal running times for solving Max CSPΓ . More precisely, we show that obtaining a running time of the form 𝒪(2 (1-ε) n ) for particular classes of Max CSP s is as hard as breaching this barrier for Max d -SAT for some d .

Adaptive Environment Generation for Continual Learning: Integrating Constraint Logic Programming with Deep Reinforcement Learning

Adaptive Environment Generation for Continual Learning: Integrating Constraint Logic Programming with Deep Reinforcement Learning

Fuzzy order-sorted feature logic

Order-Sorted Feature (OSF) logic is a knowledge representation and reasoning language based on function-denoting feature symbols and set-denoting sort symbols ordered in a subsumption lattice. OSF logic allows the construction of record-like terms that represent classes of entities and that are themselves ordered in a subsumption relation. The unification algorithm for such structures provides an efficient calculus of type subsumption, which has been applied in computational linguistics and implemented in constraint logic programming languages such as LOGIN and LIFE and automated reasoners such as CEDAR. This work generalizes OSF logic to a fuzzy setting. We give a flexible definition of a fuzzy subsumption relation which generalizes Zadeh's inclusion between fuzzy sets. Based on this definition we define a fuzzy semantics of OSF logic where sort symbols and OSF terms denote fuzzy sets. We extend the subsumption relation to OSF terms and prove that it constitutes a fuzzy partial order with the property that two OSF terms are subsumed by one another in the crisp sense if and only if their subsumption degree is greater than 0. We show how to find the greatest lower bound of two OSF terms by unifying them and how to compute the subsumption degree between two OSF terms, and we provide the complexity of these operations.

A Prolog assisted search for new simple Lie algebras

We describe some recent computer investigations with the ‘Constraint Logic Programming over Finite Domains’ library in the Prolog programming environment to search for new simple Lie algebras over the field GF ⁡ ( 2 ) \operatorname {GF}(2) of 2 2 elements. Motivated by a paper of Grishkov et al., we specifically look for those with a thin decomposition, and we settle one of their conjectures. We extrapolate from our results the existence of two new infinite families of simple Lie algebras, in addition to finding seven new sporadic examples in dimension 31 31 . We also better contextualise some previously discovered simple algebras, putting them into families which do not seem to have ever appeared in the literature, and give an updated table of those currently known.

Distributed robust optimization with coupled constraints via Tseng’s splitting method

We consider distributed robust convex optimization with both local and coupled constraints, where coefficients with respect to local constraints are uncertain in polyhedral sets. We derive an equivalent optimization model with extended decision variables and finite constraints, and characterize its optimality condition. Also, we transform the problem as finding zeros of an operator and reveal the monotonicity of the underlying operator. By employing Tseng’s operator splitting method, we design a distributed algorithm to solve the considered robust optimization problem with guaranteed convergence, and also illustrate the efficiency in numerical simulations.

RDNF Oriented Analytics to Random Boolean Functions

Dominant areas of computer science and computation systems are intensively linked to the hypercube-related studies and interpretations. This article presents some transformations and analytics for some example algorithms and Boolean domain problems. Our focus is on the methodology of complexity evaluation and integration of several types of postulations concerning special hypercube structures. Our primary goal is to demonstrate the usual formulas and analytics in this area, giving the necessary set of common formulas often used for complexity estimations and approximations. The basic example under considered is the Boolean minimization problem, in terms of the average complexity of the so-called reduced disjunctive normal form (also referred to as complete, prime irredundant, or Blake canonical form). In fact, combinatorial counterparts of the disjunctive normal form complexities are investigated in terms of sets of their maximal intervals. The results obtained compose the basis of logical separation classification algorithmic technology of pattern recognition. In fact, these considerations are not only general tools of minimization investigations of Boolean functions, but they also prove useful structures, models, and analytics for constraint logic programming, machine learning, decision policy optimization and other domains of computer science.

An Automatically Verified Prototype of the Android Permissions System

In a previous work we presented formal specifications of idealized formulations of the permission model of Android in the Coq proof assistant. This formal development is about 23 KLOC of Coq code, including proofs. In this work the Coq model is encoded in $$\{log\}$$ (‘setlog’)—a satisfiability solver and a constraint logic programming language— which is then used to automatically discharge most of the proofs performed in Coq. We show how the Coq model is encoded in $$\{log\}$$ and how automated proofs are performed. The resulting $$\{log\}$$ model is an automatically verified executable prototype of the Android permissions system. Detailed data on the empirical evaluation resulting after executing all the proofs in $$\{log\}$$ is provided. The integration of Coq and $$\{log\}$$ as to provide a framework featuring automated proof and prototype generation is discussed.

The Complexity of Network Satisfaction Problems for Symmetric Relation Algebras with a Flexible Atom

Robin Hirsch posed in 1996 the Really Big Complexity Problem: classify the computational complexity of the network satisfaction problem for all finite relation algebras A. We provide a complete classification for the case that A is symmetric and has a fexible atom; in this case, the problem is NP-complete or in P. The classification task can be reduced to the case where A is integral. If a finite integral relation algebra has a flexible atom, then it has a normal representation B. We can then study the computational complexity of the network satisfaction problem of A using the universal-algebraic approach, via an analysis of the polymorphisms of B. We also use a Ramsey-type result of Nešetřil and Rödl and a complexity dichotomy result of Bulatov for conservative finite-domain constraint satisfaction problems.

On the Descriptive Complexity of Temporal Constraint Satisfaction Problems

Finite-domain constraint satisfaction problems are either solvable by Datalog or not even expressible in fixed-point logic with counting. The border between the two regimes can be described by a universal-algebraic minor condition. For infinite-domain constraint satisfaction problems (CSPs), the situation is more complicated even if the template structure of the CSP is model-theoretically tame. We prove that there is no Maltsev condition that characterizes Datalog already for the CSPs of first-order reducts of (ℚ;<); such CSPs are called temporal CSPs and are of fundamental importance in infinite-domain constraint satisfaction. Our main result is a complete classification of temporal CSPs that can be expressed in one of the following logical formalisms: Datalog, fixed-point logic (with or without counting), or fixed-point logic with the mod-2 rank operator. The classification shows that many of the equivalent conditions in the finite fail to capture expressibility in Datalog or fixed-point logic already for temporal CSPs.

Computational Short Cuts in Infinite Domain Constraint Satisfaction

A backdoor in a finite-domain CSP instance is a set of variables where each possible instantiation moves the instance into a polynomial-time solvable class. Backdoors have found many applications in artificial intelligence and elsewhere, and the algorithmic problem of finding such backdoors has consequently been intensively studied. Sioutis and Janhunen have proposed a generalised backdoor concept suitable for infinite-domain CSP instances over binary constraints. We generalise their concept into a large class of CSPs that allow for higher-arity constraints. We show that this kind of infinite-domain backdoors have many of the positive computational properties that finite-domain backdoors have: the associated computational problems are fixed parameter tractable whenever the underlying constraint language is finite. On the other hand, we show that infinite languages make the problems considerably harder: the general backdoor detection problem is W[2]-hard and fixed-parameter tractability is ruled out under standard complexity-theoretic assumptions. We demonstrate that backdoors may have suboptimal behaviour on binary constraints—this is detrimental from an AI perspective where binary constraints are predominant in, for instance, spatiotemporal applications. In response to this, we introduce sidedoors as an alternative to backdoors. The fundamental computational problems for sidedoors remain fixed-parameter tractable for finite constraint language (possibly also containing non-binary relations). Moreover, the sidedoor approach has appealing computational properties that sometimes leads to faster algorithms than the backdoor approach.

Nash equilibrium structure of Cox process Hotelling games

AbstractWe study an N-player game where a pure action of each player is to select a nonnegative function on a Polish space supporting a finite diffuse measure, subject to a finite constraint on the integral of the function. This function is used to define the intensity of a Poisson point process on the Polish space. The processes are independent over the players, and the value to a player is the measure of the union of her open Voronoi cells in the superposition point process. Under randomized strategies, the process of points of a player is thus a Cox process, and the nature of competition between the players is akin to that in Hotelling competition games. We characterize when such a game admits Nash equilibria and prove that when a Nash equilibrium exists, it is unique and consists of pure strategies that are proportional in the same proportions as the total intensities. We give examples of such games where Nash equilibria do not exist. A better understanding of the criterion for the existence of Nash equilibria remains an intriguing open problem.

Declarative Programming with Intensional Sets in Java Using JSetL

Abstract Intensional sets are sets given by a property rather than by enumerating their elements. In a previous work, we have proposed a decision procedure for a first-order logic language which provides restricted intensional sets (RISs), i.e. a sub-class of intensional sets that are guaranteed to denote finite—though unbounded—sets. In this paper, we show how RIS can be exploited as a convenient programming tool also in a conventional setting, namely the imperative O-O language Java. We do this by considering a Java library, called JSetL, that integrates the notions of logical variable, (set) unification and constraints that are typical of constraint logic programming languages into the Java language. We show how JSetL is naturally extended to accommodate for RIS and RIS constraints and how this extension can be exploited; on the one hand, to support a more declarative style of programming and, on the other hand, to effectively enhance the expressive power of the constraint language provided by the library.

The inverse minisum circle location problem

Let n weighted points be given in the plane. The inverse version of the minisum circle location problem deals with modifying the weights of points with minimum cost, such that the sum of the weighted distances from the circumference of a given circle C with radius r, to the given points is minimized. The classical model of this problem contains infinite constraints. In this paper, a mathematical model with finite constraints is presented. Then an efficient method is developed for solving this problem.

Analysis and Transformation of Constrained Horn Clauses for Program Verification

AbstractThis paper surveys recent work on applying analysis and transformation techniques that originate in the field of constraint logic programming (CLP) to the problem of verifying software systems. We present specialization-based techniques for translating verification problems for different programming languages, and in general software systems, into satisfiability problems for constrained Horn clauses (CHCs), a term that has become popular in the verification field to refer to CLP programs. Then, we describe static analysis techniques for CHCs that may be used for inferring relevant program properties, such as loop invariants. We also give an overview of some transformation techniques based on specialization and fold/unfold rules, which are useful for improving the effectiveness of CHC satisfiability tools. Finally, we discuss future developments in applying these techniques.

Integrating Cardinality Constraints into Constraint Logic Programming with Sets

AbstractFormal reasoning about finite sets and cardinality is important for many applications, including software verification, where very often one needs to reason about the size of a given data structure. The Constraint Logic Programming tool $$\{ log\} $$ provides a decision procedure for deciding the satisfiability of formulas involving very general forms of finite sets, although it does not provide cardinality constraints. In this paper we adapt and integrate a decision procedure for a theory of finite sets with cardinality into $$\{ log\} $$ . The proposed solver is proved to be a decision procedure for its formulas. Besides, the new CLP instance is implemented as part of the $$\{ log\} $$ tool. In turn, the implementation uses Howe and King’s Prolog SAT solver and Prolog’s CLP(Q) library, as an integer linear programming solver. The empirical evaluation of this implementation based on +250 real verification conditions shows that it can be useful in practice.Under consideration in Theory and Practice of Logic Programming (TPLP)

A decision support model for handling customer orders in business chain

One of the elements of the modern trade and services market is a business chain solution (chain store/retail chain). An example of a business chain is, e.g., a restaurant chain, where each restaurant in the chain has the same decor, organization, menu, and delivery method. Although such solutions have been known for decades, the rapid development of IT technology, the widespread access to the Internet as well as the development of mobile technologies have changed and modernized their formula. Many customers place orders remotely with the option of delivery to their door. This method of ordering and fulfilling orders is becoming more and more popular and ever more common in the recent period due to the pandemic and the resulting restrictions and limitations on the functioning of trade and services. The following key questions arise in relation to customer order processing for chain business managers: How to allocate individual customer orders to selected branches so that the cost of their processing (production and delivery) is the lowest?, How to deliver on time?, etc. To answer these questions, a decision support model has been developed, which combines routing, allocation and planning problems for restaurant/store chains. Two ways to implement the model have been proposed. The first one uses the methods of mathematical modeling and programming, and the other, which is a proprietary approach that integrates the mechanisms of evolution (specialized representations, repair mechanisms, genetic operators, etc.), uses constraint logic programming and dedicated heuristics. In addition, procedures for constraint handling and presolving have been developed.