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Formal methods apply algorithms based on mathematical principles to enhance the reliability of systems. It would only be natural to try to progress from verification, model checking or testing a system against its formal specification into…
The idea of using unfolding as a way of computing a program semantics has been applied successfully to logic programs and has shown itself a powerful tool that provides concrete, implementable results, as its outcome is actually source…
Synthesis of program parts is very useful for concurrent systems. However, most synthesis approaches do not support common design tasks, like modifying a single process without having to re-synthesize or verify the whole system.…
Machine learning researchers and practitioners steadily enlarge the multitude of successful learning models. They achieve this through in-depth theoretical analyses and experiential heuristics. However, there is no known general-purpose…
In recent years, deep learning techniques have been developed to improve the performance of program synthesis from input-output examples. Albeit its significant progress, the programs that can be synthesized by state-of-the-art approaches…
Programming by Example (PBE) is the task of inducing computer programs from input-output examples. It can be seen as a type of machine learning where the hypothesis space is the set of legal programs in some programming language. Recent…
We study the following decision problem: is the language recognized by a quantum finite automaton empty or non-empty? We prove that this problem is decidable or undecidable depending on whether recognition is defined by strict or non-strict…
Large language models have shown unprecedented abilities in generating linguistically coherent and syntactically correct natural language output. However, they often return incorrect and inconsistent answers to input questions. Due to the…
Program synthesis is the task of automatically constructing a program conforming to a given specification. In this paper we focus on synthesis of single-invocation recursion-free functions conforming to a specification given as a logical…
Models of a generalized nondeterminism are defined by limitations on nonde- terministic behavior of a computing device. A regular realizability problem is a problem of verifying existence of a special sort word in a regular language. These…
The notion of non-deterministic logical matrix (where connectives are interpreted as multi-functions) preserves many good properties of traditional semantics based on logical matrices (where connectives are interpreted as functions) whilst…
We show that the decidability of the first-order theory of the language that combines Boolean algebras of sets of uninterpreted elements with Presburger arithmetic operations. We thereby disprove a recent conjecture that this theory is…
We develop a framework to give upper bounds on the "practical" computational complexity of stability problems for a wide range of nonlinear continuous and hybrid systems. To do so, we describe stability properties of dynamical systems using…
Probabilistic programs are key to deal with uncertainty in e.g. controller synthesis. They are typically small but intricate. Their development is complex and error prone requiring quantitative reasoning over a myriad of alternative…
We consider the two categories of termination problems of quantum programs with nondeterminism: 1) Is an input of a program terminating with probability one under all schedulers? If not, how can a scheduler be synthesized to evidence the…
We consider the problem of establishing that a program-synthesis problem is unrealizable (i.e., has no solution in a given search space of programs). Prior work on unrealizability has developed some automatic techniques to establish that a…
We study the model-checking problem for recursion schemes: does the tree generated by a given higher-order recursion scheme satisfy a given logical sentence. The problem is known to be decidable for sentences of the MSO logic. We prove…
In this paper, we investigate the problem of synthesizing computable functions of infinite words over an infinite alphabet (data omega-words). The notion of computability is defined through Turing machines with infinite inputs which can…
We study discrete probabilistic programs with potentially unbounded looping behaviors over an infinite state space. We present, to the best of our knowledge, the first decidability result for the problem of determining whether such a…
The combination of Large Language Models (LLMs), systematic evaluation, and evolutionary algorithms has enabled breakthroughs in combinatorial optimization and scientific discovery. We propose to extend this powerful combination to the…