Related papers: Automated Induction for Complex Data Structures
We introduce constraints necessary for type checking a higher-order concurrent constraint language, and solve them with an incremental algorithm. Our constraint system extends rational unification by constraints x$\subseteq$ y saying that…
We consider the problem of automatically verifying programs which manipulate arbitrary data structures. Our specification language is expressive, contains a notion of \emph{separation}, and thus enables a precise specification of…
The focus of this paper is the analysis of real-time systems with recursion, through the development of good theoretical techniques which are implementable. Time is modeled using clock variables, and recursion using stacks. Our technique…
Traditional automated theorem provers for first-order logic depend on speed-optimized search and many handcrafted heuristics that are designed to work best over a wide range of domains. Machine learning approaches in literature either…
We present a sequent-based deductive system for automatically proving entailments in separation logic by using mathematical induction. Our technique, called mutual explicit induction proof, is an instance of Noetherian induction.…
The definition is a common form of human expert knowledge, a building block of formal science and mathematics, a foundation for database theory and is supported in various forms in many knowledge representation and formal specification…
Concept Induction refers to the problem of creating complex Description Logic class descriptions (i.e., TBox axioms) from instance examples (i.e., ABox data). In this paper we look particularly at the case where both a set of positive and a…
Using multisets, we develop novel techniques for mechanizing the proofs of the synthesis conjectures for list-sorting algorithms, and we demonstrate them in the Theorema system. We use the classical principle of extracting the algorithm as…
The intention of the present study is to establish the mathematical fundamentals for automated problem solving essentially targeted for robotics by approaching the task universal algebraically introducing knowledge as realizations of…
Viewing formal mathematical proofs as logical terms provides a powerful and elegant basis for analyzing how human experts tend to structure proofs and how proofs can be structured by automated methods. We pursue this approach by (1)…
Indexed languages are a classical notion in formal language theory, which has attracted attention in recent decades due to its role in higher-order model checking: They are precisely the languages accepted by order-2 pushdown automata. The…
The automated generation of exercises may substantially reduce the time educators devote to manual exercise design. A major obstacle to the integration of such automation into teaching practice, however, lies in the ability to control the…
This paper introduces a new algorithm for the induction if complex finite state automata from samples of behavior. The algorithm is based on information theoretic principles. The algorithm reduces the search space by many orders of…
We study induction on the program structure as a proof method for bisimulation-based compiler correctness. We consider a first-order language with mutually recursive function definitions, system calls, and an environment semantics. The…
The tree automaton completion is an algorithm used for proving safety properties of systems that can be modeled by a term rewriting system. This representation and verification technique works well for proving properties of infinite systems…
In this position paper, we propose a reasoning framework that can model the reasoning process underlying natural language inferences. The framework is based on the semantic tableau method, a well-studied proof system in formal logic. Like…
By algorithmic metatheorems for a model checking problem P over infinite-state systems we mean generic results that can be used to infer decidability (possibly complexity) of P not only over a specific class of infinite systems, but over a…
We consider the problem of explaining the predictions of an arbitrary blackbox model $f$: given query access to $f$ and an instance $x$, output a small set of $x$'s features that in conjunction essentially determines $f(x)$. We design an…
We propose abstract compilation for precise static type analysis of object-oriented languages based on coinductive logic programming. Source code is translated to a logic program, then type-checking and inference problems amount to queries…
We propose a framework for reasoning about programs that manipulate coinductive data as well as inductive data. Our approach is based on using equational programs, which support a seamless combination of computation and reasoning, and using…