Related papers: Decidable Synthesis of Programs with Uninterpreted…
Many real applications problems can be encoded easily as quantified formulas in SMT. However, this simplicity comes at the cost of difficulty during solving by SMT solvers. Different strategies and quantifier instantiation techniques have…
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 give extensional and intensional characterizations of functional programs with nondeterminism: as structure preserving functions between biorders, and as nondeterministic sequential algorithms on ordered concrete data structures which…
We construct a finitely presented group with undecidable word problem and with Dehn function bounded by a quadratic function on an infinite set of positive integers.
Program synthesis aims to automatically construct human-readable programs that satisfy given task specifications, such as input/output pairs or demonstrations. Recent works have demonstrated encouraging results in a variety of domains, such…
Proving Unrealizability for Syntax-Guided Synthesis We consider the problem of automatically establishing that a given syntax-guided-synthesis (SyGuS) problem is unrealizable (i.e., has no solution). Existing techniques have quite limited…
We show that strict deterministic propositional dynamic logic with intersection is highly undecidable, solving a problem in the Stanford Encyclopedia of Philosophy. In fact we show something quite a bit stronger. We introduce the…
Program synthesis is the task of automatically generating expressions that satisfy a given specification. Program synthesis techniques have been used to automate the generation of loop invariants in code, synthesize function summaries, and…
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…
Transductions are binary relations of finite words. For rational transductions, i.e., transductions defined by finite transducers, the inclusion, equivalence and sequential uniformisation problems are known to be undecidable. In this paper,…
We present and study new definitions of universal and programmable universal unary functions and consider a new simplicity criterion: almost decidability of the halting set. A set of positive integers S is almost decidable if there exists a…
Answer set programming - the most popular problem solving paradigm based on logic programs - has been recently extended to support uninterpreted function symbols. All of these approaches have some limitation. In this paper we propose a…
In recent years, deep learning has made tremendous progress in a number of fields that were previously out of reach for artificial intelligence. The successes in these problems has led researchers to consider the possibilities for…
We study the reactive synthesis problem (RS) for specifications given in Metric Interval Temporal Logic (MITL). RS is known to be undecidable in a very general setting, but on infinite words only; and only the very restrictive BRRS subcase…
Disjunctive finitary programs are a class of logic programs admitting function symbols and hence infinite domains. They have very good computational properties, for example ground queries are decidable while in the general case the stable…
We study decidability of verification problems for timed automata extended with unbounded discrete data structures. More detailed, we extend timed automata with a pushdown stack. In this way, we obtain a strong model that may for instance…
Program synthesis is the process of automatically translating a specification into computer code. Traditional synthesis settings require a formal, precise specification. Motivated by computer education applications where a student learns to…
We present a method for synthesizing recursive functions that satisfy both a functional specification and an asymptotic resource bound. Prior methods for synthesis with a resource metric require the user to specify a concrete expression…
Program verification and synthesis frameworks that allow one to customize the language in which one is interested typically require the user to provide a formally defined semantics for the language. Because writing a formal semantics can be…
We consider expressions built up from binary relation names using the operators union, composition, and set difference. We show that it is undecidable to test whether a given such expression $e$ is finitely satisfiable, i.e., whether there…