Related papers: Certified Symbolic Finite Transducers: Formalizati…
Regular string-to-string functions enjoy a nice triple characterization through deterministic two-way transducers (2DFT), streaming string transducers (SST) and MSO definable functions. This result has recently been lifted to FO definable…
Autoformalization, the task of automatically translating natural language descriptions into a formal language, poses a significant challenge across various domains, especially in mathematics. Recent advancements in large language models…
Autoformalization is the process of automatically translating from natural language mathematics to formal specifications and proofs. A successful autoformalization system could advance the fields of formal verification, program synthesis,…
Stepwise refinement of algebraic specifications is a well known formal methodology for program development. However, traditional notions of refinement based on signature morphisms are often too rigid to capture a number of relevant…
Speech processing requires very efficient methods and algorithms. Finite-state transducers have been shown recently both to constitute a very useful abstract model and to lead to highly efficient time and space algorithms in this field. We…
This article describes an algorithm for reducing the intermediate alphabets in cascades of finite-state transducers (FSTs). Although the method modifies the component FSTs, there is no change in the overall relation described by the whole…
In Formal Languages and Automata Theory courses, students find understanding nondeterministic finite-state and pushdown automata difficult. In many cases, this means that it is challenging for them to comprehend the operational semantics of…
The transducer synthesis problem on finite words asks, given a specification $S \subseteq I \times O$, where $I$ and $O$ are sets of finite words, whether there exists an implementation $f: I \rightarrow O$ which (1) fulfils the…
Dynamic Fault Trees (DFTs) is a widely used failure modeling technique that allows capturing the dynamic failure characteristics of systems in a very effective manner. Simulation and model checking have been traditionally used for the…
A quantum finite-state automaton (QFA) is a theoretical model designed to simulate the evolution of a quantum system with finite memory in response to sequential input strings. We define the language of a QFA as the set of strings that lead…
A recent paper by Drewes, Hoffmann, and Minas (GCM 2023 proceedings) has shown that certain graph languages can be defined and efficiently recognized by finite automata when strings over typed symbols are interpreted as graphs. This…
Proof assistants are important tools for teaching logic. We support this claim by discussing three formalizations in Isabelle/HOL used in a recent course on automated reasoning. The first is a formalization of System W (a system of…
Reliable verification of proofs remains a bottleneck for training and evaluating AI systems on hard mathematical reasoning. Fully formal proofs, in languages like Lean, are easy to verify because they are unambiguous and modular. Most…
We consider the formulation of a symbolic execution (SE) procedure for functional programs that interact with effectful, opaque libraries. Our procedure allows specifications of libraries and abstract data type (ADT) methods that are…
We formally verify an algorithm for approximate policy iteration on Factored Markov Decision Processes using the interactive theorem prover Isabelle/HOL. Next, we show how the formalized algorithm can be refined to an executable, verified…
Automating string transformations has been one of the killer applications of program synthesis. Existing synthesizers that solve this problem produce programs in domain-specific languages (DSL) that are engineered to help the synthesizer,…
Feature Structures (FSs) are a widespread tool used for decompositional frameworks of Attribute-Value associations. Even though they thrive in simple systems, they lack a way of representing higher-order entities and relations. This is…
We present a general model allowing static analysis based on abstract interpretation for systems of communicating processes. Our technique, inspired by Regular Model Checking, represents set of program states as lattice automata and…
Translating formulas of Linear Temporal Logic (LTL) over finite traces, or LTLf, to symbolic Deterministic Finite Automata (DFA) plays an important role not only in LTLf synthesis, but also in synthesis for Safety LTL formulas. The…
The growing complexity and diversity of models used in the engineering of dependable systems implies that a variety of formal methods, across differing abstractions, paradigms, and presentations, must be integrated. Such an integration…