arXiv subjects

Paul Krogmeier

Publications and source records attributed to Paul Krogmeier.

7 recordsLinked to original sources

arXiv2025

Synthesizing DSLs for Few-Shot Learning

We study the problem of synthesizing domain-specific languages (DSLs) for few-shot learning in symbolic domains. Given a base language and instances of few-shot learning problems, where each instance is split into training and testing samples, the DSL synthesis problem asks for a grammar over the base language that guarantees that small expressions solving training samples also solve corresponding testing samples. We prove that the problem is decidable for a class of languages whose semantics over fixed structures can be evaluated by tree automata and when expression size corresponds to parse tree depth in the grammar, and, furthermore, the grammars solving the problem correspond to a regular set of trees. We also prove decidability results for variants of the problem where DSLs are only required to express solutions for input learning problems and where DSLs are defined using macro grammars.

cs.PL↗

arXiv2023

Languages with Decidable Learning: A Meta-theorem

We study expression learning problems with syntactic restrictions and introduce the class of finite-aspect checkable languages to characterize symbolic languages that admit decidable learning. The semantics of such languages can be defined using a bounded amount of auxiliary information that is independent of expression size but depends on a fixed structure over which evaluation occurs. We introduce a generic programming language for writing programs that evaluate expression syntax trees, and we give a meta-theorem that connects such programs for finite-aspect checkable languages to finite tree automata, which allows us to derive new decidable learning results and decision procedures for several expression learning problems by writing programs in the programming language.

cs.LO↗

arXiv2021

Learning Formulas in Finite Variable Logics

We consider grammar-restricted exact learning of formulas and terms in finite variable logics. We propose a novel and versatile automata-theoretic technique for solving such problems. We first show results for learning formulas that classify a set of positively- and negatively-labeled structures. We give algorithms for realizability and synthesis of such formulas along with upper and lower bounds. We also establish positive results using our technique for other logics and variants of the learning problem, including first-order logic with least fixed point definitions, higher-order logics, and synthesis of queries and terms with recursively-defined functions.

cs.LO↗

arXiv2020

Deciding Accuracy of Differential Privacy Schemes

Differential privacy is a mathematical framework for developing statistical computations with provable guarantees of privacy and accuracy. In contrast to the privacy component of differential privacy, which has a clear mathematical and intuitive meaning, the accuracy component of differential privacy does not have a generally accepted definition; accuracy claims of differential privacy algorithms vary from algorithm to algorithm and are not instantiations of a general definition. We identify program discontinuity as a common theme in existing \emph{ad hoc} definitions and introduce an alternative notion of accuracy parametrized by, what we call, {\distance} -- the {\distance} of an input $x$ w.r.t., a deterministic computation $f$ and a distance $d$, is the minimal distance $d(x,y)$ over all $y$ such that $f(y)\neq f(x)$. We show that our notion of accuracy subsumes the definition used in theoretical computer science, and captures known accuracy claims for differential privacy algorithms. In fact, our general notion of accuracy helps us prove better claims in some cases. Next, we study the decidability of accuracy. We first show that accuracy is in general undecidable. Then, we define a non-trivial class of probabilistic computations for which accuracy is decidable (unconditionally, or assuming Schanuel's conjecture). We implement our decision procedure and experimentally evaluate the effectiveness of our approach for generating proofs or counterexamples of accuracy for common algorithms from the literature.

cs.CR↗

arXiv2020

Decidable Synthesis of Programs with Uninterpreted Functions

We identify a decidable synthesis problem for a class of programs of unbounded size with conditionals and iteration that work over infinite data domains. The programs in our class use uninterpreted functions and relations, and abide by a restriction called coherence that was recently identified to yield decidable verification. We formulate a powerful grammar-restricted (syntax-guided) synthesis problem for coherent uninterpreted programs, and we show the problem to be decidable, identify its precise complexity, and also study several variants of the problem.

cs.PL↗

arXiv2019

Deciding Memory Safety for Single-Pass Heap-Manipulating Programs

We investigate the decidability of automatic program verification for programs that manipulate heaps, and in particular, decision procedures for proving memory safety for them. We extend recent work that identified a decidable subclass of uninterpreted programs to a class of alias-aware programs that can update maps. We apply this theory to develop verification algorithms for memory safety--- determining if a heap-manipulating program that allocates and frees memory locations and manipulates heap pointers does not dereference an unallocated memory location. We show that this problem is decidable when the initial allocated heap forms a forest data-structure and when programs are streaming-coherent, which intuitively restricts programs to make a single pass over a data-structure. Our experimental evaluation on a set of library routines that manipulate forest data-structures shows that common single-pass algorithms on data-structures often fall in the decidable class, and that our decision procedure is efficient in verifying them.

cs.PL↗

arXiv2019

Composing Neural Learning and Symbolic Reasoning with an Application to Visual Discrimination

We consider the problem of combining machine learning models to perform higher-level cognitive tasks with clear specifications. We propose the novel problem of Visual Discrimination Puzzles (VDP) that requires finding interpretable discriminators that classify images according to a logical specification. Humans can solve these puzzles with ease and they give robust, verifiable, and interpretable discriminators as answers. We propose a compositional neurosymbolic framework that combines a neural network to detect objects and relationships with a symbolic learner that finds interpretable discriminators. We create large classes of VDP datasets involving natural and artificial images and show that our neurosymbolic framework performs favorably compared to several purely neural approaches.

cs.LG↗