The classic theorems of Büchi and Kleene state the expressive equivalence of finite automata to monadic second order logic and regular expressions, respectively. These fundamental results enjoy applications in nearly every field of theoretical computer science. Around the same time as Büchi and Kleene, Rabin investigated probabilistic finite automata. This equally well established model has applications ranging from natural language processing to probabilistic model checking. Here, we give probabilistic extensions Büchi\\\'s theorem and Kleene\\\'s theorem to the probabilistic setting. We obtain a probabilistic MSO logic by adding an expected second order quantifier. In the scope of this quantifier, membership is determined by a Bernoulli process. This approach turns out to be universal and is applicable for finite and infinite words as well as for finite trees. In order to prove the expressive equivalence of this probabilistic MSO logic to probabilistic automata, we show a Nivat-theorem, which decomposes a recognisable function into a regular language, homomorphisms, and a probability measure. For regular expressions, we build upon existing work to obtain probabilistic regular expressions on finite and infinite words. We show the expressive equivalence between these expressions and probabilistic Muller-automata. To handle Muller-acceptance conditions, we give a new construction from probabilistic regular expressions to Muller-automata. Concerning finite trees, we define probabilistic regular tree expressions using a new iteration operator, called infinity-iteration. Again, we show that these expressions are expressively equivalent to probabilistic tree automata. On a second track of our research we investigate Constraint LTL over multidimensional data words with data values from the infinite tree. Such LTL formulas are evaluated over infinite words, where every position possesses several data values from the infinite tree. Within Constraint LTL on can compare these values from different positions. We show that the model checking problem for this logic is PSPACE-complete via investigating the emptiness problem of Constraint Büchi automata.

<p>Quite often modelers with constraint programming (CP) use the same modelling patterns for different problems, possibly from different domains. This results in recurring idioms in constraint programs. Our approach can be seen as a three-step approach. First, we identify some of these recurring patterns in constraint programs. Second, we propose a general way of describing these patterns by introducing proper constructs that would cover a wide range of applications. Third, we propose automating the process of reproducing these idioms from these higher-level descriptions. The whole process can be seen as a way of encapsulating some of the expertise and knowledge often used by CP modelers and making it available in much simpler forms. Doing so, we are able to extend current CP languages with high-level abstractions that open doors for automation of some of the modelling processes.</p><p>In particular, we introduce function variables and allow the statement of constraints on these variables using function operations. A <i>function variable</i> is a decision variable that can take a value from a set of functions as opposed to an <i>integer variable</i> that ranges over integers, or a <i>set variable</i> that ranges over a set of sets. We show that a function variable can be mapped into different representations in terms of integer and set variables, and illustrate how to map constraints stated on a function variable into constraints on integer and set variables. As a result, a function model expressed using function variables opens doors to the automatic generation of alternate CP models. These alternate models either use a different variable representation, or have extra implied constraints, or employ different constraint formulation, or combine different models that are linked using channelling constraints. A number of heuristics are also developed that allow the comparison of different constraint formulations. Furthermore, we present an extensive theoretical comparison of models of injection problems supported by asymptotic and empirical studies. Finally, a practical modelling tool that is built based on a high-level language that allows function variables is presented and evaluated. The tool helps users explore different alternate CP models starting from a function model that is easier to develop, understand, and maintain.</p>

<p>Many problems in business, industry, and academia can be modelled as constraint programs consisting of matrices of decision variables. Such “matrix models” often have symmetry. In particular, they often have row and column symmetry as the rows and columns can freely be permuted without affecting the satisfiability of assignments. Existing methods have difficulty in dealing with the super-exponential number of symmetries in a problem with row and column symmetry. We therefore propose some ordering constraints which can effectively break such symmetries. To use these constraints in practice, we develop some efficient linear time propagators. We demonstrate the effectiveness of these symmetry breaking ordering constraints on a wide range of problems. We also show how such ordering constraints can be used to deal with partial symmetries, as well as value symmetries.</p>

While there are efforts to establish a single international accounting standard, there are strong current and future needs to handle heterogeneous accounting methods and systems. We advocate a context-based approach to dealing with multiple accounting standards and equational ontological conflicts. In this paper we first define what we mean by equational ontological conflicts and then describe a new approach, using Constraint Logic Programming and abductive reasoning, to reconcile such conflicts among disparate information systems. In particular, we focus on the use of Constraint Handling Rules as a simultaneous symbolic equation solver, which is a powerful way to combine, invert and simplify multiple conversion functions that translate between different contexts. Finally, we demonstrate a sample application using our prototype implementation that demonstrates the viability of our approach. / Singapore-MIT Alliance (SMA)

Quite often modelers with constraint programming (CP) use the same modelling patterns for different problems, possibly from different domains. This results in recurring idioms in constraint programs. Our approach can be seen as a three-step approach. First, we identify some of these recurring patterns in constraint programs. Second, we propose a general way of describing these patterns by introducing proper constructs that would cover a wide range of applications. Third, we propose automating the process of reproducing these idioms from these higher-level descriptions. The whole process can be seen as a way of encapsulating some of the expertise and knowledge often used by CP modelers and making it available in much simpler forms. Doing so, we are able to extend current CP languages with high-level abstractions that open doors for automation of some of the modelling processes. In particular, we introduce function variables and allow the statement of constraints on these variables using function operations. A function variable is a decision variable that can take a value from a set of functions as opposed to an integer variable that ranges over integers, or a set variable that ranges over a set of sets. We show that a function variable can be mapped into different representations in terms of integer and set variables, and illustrate how to map constraints stated on a function variable into constraints on integer and set variables. As a result, a function model expressed using function variables opens doors to the automatic generation of alternate CP models. These alternate models either use a different variable representation, or have extra implied constraints, or employ different constraint formulation, or combine different models that are linked using channelling constraints. A number of heuristics are also developed that allow the comparison of different constraint formulations. Furthermore, we present an extensive theoretical comparison of models of injection problems supported by asymptotic and empirical studies. Finally, a practical modelling tool that is built based on a high-level language that allows function variables is presented and evaluated. The tool helps users explore different alternate CP models starting from a function model that is easier to develop, understand, and maintain.

Many problems in business, industry, and academia can be modelled as constraint programs consisting of matrices of decision variables. Such “matrix models” often have symmetry. In particular, they often have row and column symmetry as the rows and columns can freely be permuted without affecting the satisfiability of assignments. Existing methods have difficulty in dealing with the super-exponential number of symmetries in a problem with row and column symmetry. We therefore propose some ordering constraints which can effectively break such symmetries. To use these constraints in practice, we develop some efficient linear time propagators. We demonstrate the effectiveness of these symmetry breaking ordering constraints on a wide range of problems. We also show how such ordering constraints can be used to deal with partial symmetries, as well as value symmetries.

Today, unified modeling language (UML) has become a standard modeling language in object-oriented systems analysis and design. Specifying the business logic constraint with object constraint language (OCL) and transforming the specification into code has become a main trend in this area. This research presents a classification of OCL expressions to specify the attribute, operation and relationship constraint on Class diagram. A sample case and a CASE tool are used to test the usability (including the concepts, application, and advantages) of the proposed method. With this approach, the system developer can specify the constraints easily and transform them into code automatically and thereby enhance the efficiency and reusability of system development.

The thesis is mainly a study on the Flexible Print Circuit which was producing manufactured. The research investigates how the FPC operates based on related product capacity data in the conjunction of back end MPS system data of producing scheduling database. Due to system and relative data collocation, it helps a salesman to make a better judgment on the outcome of an order before making promises to customers. In addition, this paper is looking into how applying the related production management method increases the number of the entire production and improves the efficiency on the production line. Then it studies how using this method can temporarily meet the needs of customers¡¦ big orders & cut-in orders before promising customers the date of delivery. Regarding manufacturing procedure of FPC, the purpose for increasing actual output is achieving the maximum production capability and the best arranging procedure. All information was given by different groups of employees from FPC industry, including its Sales Department, Production Management Department, Procurement Department and Supply Department; it also derives from the interviews with station managers and high level managers. With situation simulation and case simulation will be revised on current product line¡¦s output and try to bring up production operation model of FPC Industry. Finally, changing production management and station order to achieve its maximum production on FPC.

Constraint Programming (CP) is a powerful technique for solving a variety of combinatorial problems. Automated modelling using a refinement based approach abstracts over modelling decisions in CP by allowing users to specify their problem in a high level specification language such as ESSENCE. This refinement process produces many models resulting from different choices that can be selected, each with their own strengths. A parameterised specification represents a problem class where the parameters of the class define the instance of the class we wish to solve. Since each model has different performance characteristics the model chosen is crucial to be able to solve the instance effectively. This thesis presents a method to generate instances automatically for the purpose of choosing a subset of the available models that have superior performance across the instance space. The second contribution of this thesis is a framework to automate the testing of a toolchain for automated modelling. This process includes a generator of test cases that covers all aspects of the ESSENCE specification language. This process utilises our first contribution namely instance generation to generate parameterised specifications. This framework can detect errors such as inconsistencies in the model produced during the refinement process. Once we have identified a specification that causes an error, this thesis presents our third contribution; a method for reducing the specification to a much simpler form, which still exhibits a similar error. Additionally this process can generate a set of complementary specifications including specifications that do not cause the error to help pinpoint the root cause.

A constraint is a formula in first-order logic expressing a relation between values of various domains. In order to solve a constraint, constructing a propositional encoding is a successfully applied technique that benefits from substantial progress made in the development of modern SAT solvers. However, propositional encodings are generally created by developing a problem-specific generator program or by crafting them manually, which often is a time-consuming and error-prone process especially for constraints over complex domains. Therefore, the present thesis introduces the constraint solver CO4 that automatically generates propositional encodings for constraints over structured finite domains written in a syntactical subset of the functional programming language Haskell. This subset of Haskell enables the specification of expressive and concise constraints by supporting user-defined algebraic data types, pattern matching, and polymorphic types, as well as higher-order and recursive functions. The constraint solver CO4 transforms a constraint written in this high-level language into a propositional formula. After an external SAT solver determined a satisfying assignment for the variables in the generated formula, a solution in the domain of discourse is derived. This approach is even applicable for finite restrictions of recursively defined algebraic data types. The present thesis describes all aspects of CO4 in detail: the language used for specifying constraints, the solving process and its correctness, as well as exemplary applications of CO4.