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In stepwise derivations of programs from specifications, data type refinements are common. Many data type refinements involve isomorphic mappings between the more abstract and more concrete data representations. Examples include refinement…
The monadic shallow linear Horn fragment is well-known to be decidable and has many application, e.g., in security protocol analysis, tree automata, or abstraction refinement. It was a long standing open problem how to extend the fragment…
Set constraints provide a highly general way to formulate program analyses. However, solving arbitrary boolean combinations of set constraints is NEXPTIME-hard. Moreover, while theoretical algorithms to solve arbitrary set constraints…
We prove an algebraic preservation theorem for positive Horn definability in aleph-zero categorical structures. In particular, we define and study a construction which we call the periodic power of a structure, and define a periomorphism of…
Determinisation and completion of finite tree automata are important operations with applications in program analysis and verification. However, the complexity of the classical procedures for determinisation and completion is high. They are…
Recent results show that a constraint satisfaction problem (CSP) defined over rational numbers with their natural ordering has a solution if and only if it has a definable solution. The proof uses advanced results from topology and modern…
Solution and analysis of mathematical programming problems may be simplified when these problems are symmetric under appropriate linear transformations. In particular, a knowledge of the symmetries may help reduce the problem dimension, cut…
Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…
One of the central open problems to classify the computational complexity of finite-domain constraint satisfaction problems within P is to prove better algorithmic results for CSPs with a Maltsev polymorphism; we do not even know whether…
Decision trees are popular machine learning models that are simple to build and easy to interpret. Even though algorithms to learn decision trees date back to almost 50 years, key properties affecting their generalization error are still…
Big data refers to large and complex data sets that, under existing approaches, exceed the capacity and capability of current compute platforms, systems software, analytical tools and human understanding. Numerous lessons on the scalability…
Algorithms which learn environments represented by automata in the past have had complexity scaling with the number of states in the automaton, which can be exponentially large even for automata recognizing regular expressions with a small…
Recursive algebraic data types (term algebras, ADTs) are one of the most well-studied theories in logic, and find application in contexts including functional programming, modelling languages, proof assistants, and verification. At this…
We study abduction in First Order Horn logic theories where all atoms can be abduced and we are looking for preferred solutions with respect to three objective functions: cardinality minimality, coherence, and weighted abduction. We…
Connected acyclic graphs (trees) are data objects that hierarchically organize categories. Collections of trees arise in a diverse variety of fields, including evolutionary biology, public health, machine learning, social sciences and…
Hierarchical text classification (HTC) depends on taxonomies that organize labels into structured hierarchies. However, many real-world taxonomies introduce ambiguities, such as identical leaf names under similar parent nodes, which prevent…
Despite massive investments in scale, deep models for click-through rate (CTR) prediction often exhibit rapidly diminishing returns - a stark contrast to the smooth, predictable gains seen in large language models. We identify the root…
We develop a spatial branch-and-cut approach for nonconvex Quadratically Constrained Quadratic Programs with bounded complex variables (CQCQP). Linear valid inequalities are added at each node of the search tree to strengthen semidefinite…
Modern software for propositional satisfiability problems gives a powerful automated reasoning toolkit, capable of outputting not only a satisfiable/unsatisfiable signal but also a justification of unsatisfiability in the form of resolution…
Commutativity has proven to be a powerful tool in reasoning about concurrent programs. Recent work has shown that a commutativity-based reduction of a program may admit simpler proofs than the program itself. The framework of…