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Concurrent systems are notoriously difficult to analyze, and technological advances such as weak memory architectures greatly compound this problem. This has renewed interest in partial order semantics as a theoretical foundation for formal…
Constraint programming uses enumeration and search tree pruning to solve combinatorial optimization problems. In order to speed up this solution process, we investigate the use of semidefinite relaxations within constraint programming. In…
An (encoded) decision problem is a pair (E, F) where E=words that encode instances of the problem, F=words to be accepted. We use "strings" in a technical sense. With an NP problem (E, F) we associate the "logogram" of F relative to E,…
We consider ways to construct a transducer for a given set of input word to output symbol pairs. This is motivated by the need for representing game playing programs in a low-level mathematical format that can be analyzed by algebraic…
Sorting networks are oblivious sorting algorithms with many practical applications and rich theoretical properties. Propositional encodings of sorting networks are a key tool for proving concrete bounds on the minimum number of comparators…
Modern software is constantly changing. Researchers and practitioners are increasingly aware that verification tools can be impactful if they embrace change through analyses that are compositional and span program versions. Reasoning about…
The emergence of large-language models (LLMs) has enabled a new class of semantic data processing systems (SDPSs) to support declarative queries against unstructured documents. Existing SDPSs are, however, lacking a unified algebraic…
To represent anything from mathematical concepts to real-world objects, we have to resort to an encoding. Encodings, such as written language, usually assume a decoder that understands a rich shared code. A semantic embedding is a form of…
A new stream of research was born in the last decade with the goal of mining itemsets of interest using Constraint Programming (CP). This has promoted a natural way to combine complex constraints in a highly flexible manner. Although CP…
We present Searn, an algorithm for integrating search and learning to solve complex structured prediction problems such as those that occur in natural language, speech, computational biology, and vision. Searn is a meta-algorithm that…
There are a huge number of problems, from various areas, being solved by reducing them to SAT. However, for many applications, translation into SAT is performed by specialized, problem-specific tools. In this paper we describe a new system…
Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
Semidefinite programs are convex optimisation problems involving a linear objective function and a domain of positive semidefinite matrices. Over the last two decades, they have become an indispensable tool in quantum information science.…
We develop the representation theory of a finite semigroup over an arbitrary commutative semiring with unit, in particular classifying the irreducible and minimal representations. The results for an arbitrary semiring are as good as the…
Human vision is able to compensate imperfections in sensory inputs from the real world by reasoning based on prior knowledge about the world. Machine learning has had a significant impact on computer vision due to its inherent ability in…
As machine learning is increasingly used to help make decisions, there is a demand for these decisions to be explainable. Arguably, the most explainable machine learning models use decision rules. This paper focuses on decision sets, a type…
Synthesizing programs using example input/outputs is a classic problem in artificial intelligence. We present a method for solving Programming By Example (PBE) problems by using a neural model to guide the search of a constraint logic…
In computational complexity theory, a decision problem is NP-complete when it is both in NP and NP-hard. Although a solution to a NP-complete can be verified quickly, there is no known algorithm to solve it in polynomial time. There exists…
We improve the backward compatibility of stableKanren to run miniKanren programs. stableKanren is a miniKanren extension capable of non-monotonic reasoning through stable model semantics. However, standard miniKanren programs that produce…
In this paper we construct a hierarchy of multivariate polynomial approximation kernels via semidefinite programming. We give details on the implementation of the semidefinite programs defining the kernels. Finally, we show how a symmetry…