Related papers: Mechanized Undecidability of Higher-order beta-Mat…
The inhabitation problem for intersection types in the lambda-calculus is known to be undecidable. We study the problem in the case of non-idempotent intersection, considering several type assignment systems, which characterize the solvable…
Higher-order pushdown systems and ground tree rewriting systems can be seen as extensions of suffix word rewriting systems. Both classes generate infinite graphs with interesting logical properties. Indeed, the model-checking problem for…
Dependent Object Types (DOT) is a calculus with path dependent types, intersection types, and object self-references, which serves as the core calculus of Scala 3. Although the calculus has been proven sound, it remains open whether type…
A decidability proof for bisimulation equivalence of first-order grammars is given. It is an alternative proof for a result by S\'enizergues (1998, 2005) that subsumes his affirmative solution of the famous decidability question for…
Motivated by applications in automated verification of higher-order functional programs, we develop a notion of constrained Horn clauses in higher-order logic and a decision problem concerning their satisfiability. We show that, although…
The static dependency pair method is a method for proving the termination of higher-order rewrite systems a la Nipkow. It combines the dependency pair method introduced for first-order rewrite systems with the notion of strong computability…
We show that equivalence of deterministic top-down tree-to-string transducers is decidable, thus solving a long standing open problem in formal language theory. We also present efficient algorithms for subclasses: polynomial time for total…
Much of human knowledge sits in large databases of unstructured text. Leveraging this knowledge requires algorithms that extract and record metadata on unstructured text documents. Assigning topics to documents will enable intelligent…
This paper investigates the decidability of opacity in timed automata (TA), a property that has been proven to be undecidable in general. First, we address a theoretical gap in recent work by J. An et al. (FM 2024) by providing necessary…
We prove several decidability and undecidability results for the satisfiability and validity problems for languages that can express solutions to word equations with length constraints. The atomic formulas over this language are equality…
In this paper we describe how to leverage higher-order unification to type check a dependently typed language with meta-variables. The literature usually presents the unification algorithm as a standalone component, however the need to…
We present a new recommendation setting for picking out two items from a given set to be highlighted to a user, based on contextual input. These two items are presented to a user who chooses one of them, possibly stochastically, with a bias…
The multi-armed bandit (MAB) problem is a foundational framework in sequential decision-making under uncertainty, extensively studied for its applications in areas such as clinical trials, online advertising, and resource allocation.…
Combining higher-order abstract syntax and (co)induction in a logical framework is well known to be problematic. Previous work described the implementation of a tool called Hybrid, within Isabelle HOL, which aims to address many of these…
The origin semantics for transducers was proposed in 2014, and led to various characterizations and decidability results that are in contrast with the classical semantics. In this paper we add a further decidability result for…
A pattern $\alpha$ is a string of variables and terminal letters. We say that $\alpha$ matches a word $w$, consisting only of terminal letters, if $w$ can be obtained by replacing the variables of $\alpha$ by terminal words. The matching…
Developing efficient sequential bidding strategies for repeated auctions is an important practical challenge in various marketing tasks. In this setting, the bidding agent obtains information, on both the value of the item at sale and the…
We present a new approach to automated reasoning about higher-order programs by endowing symbolic execution with a notion of higher-order, symbolic values. Our approach is sound and relatively complete with respect to a first-order solver…
We solve a well known and long-standing open problem in database theory, proving that Conjunctive Query Finite Determinacy Problem is undecidable. The technique we use builds on the top of our Red Spider method which we developed in our…
Using a novel rewriting problem, we show that several natural decision problems about finite automata are undecidable (i.e., recursively unsolvable). In contrast, we also prove three related problems are decidable. We apply one result to…