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This paper studies Linear Temporal Logic over Finite Traces (LTLf) where proposition letters are replaced with first-order formulas interpreted over arbitrary theories, in the spirit of Satisfiability Modulo Theories. The resulting logic,…
The class of uniformly computable real functions with respect to a small subrecursive class of operators computes the elementary functions of calculus, restricted to compact subsets of their domains. The class of conditionally computable…
Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…
Bidirectional typechecking, in which terms either synthesize a type or are checked against a known type, has become popular for its scalability (unlike Damas-Milner type inference, bidirectional typing remains decidable even for very…
Most ideas about what an algorithm is are very similar. Basic operations are used for transforming objects. The evaluation of internal and external states by relations has impact on the further process. A more precise definition can lead to…
A decidable transfinite hierarchy is defined by assigning ordinals to the programs of an imperative language. It singles out: the classes TIMEF(n^c) and TIMEF(n_c); the finite Grzegorczyk classes at and above the elementary level, and the…
A syntactical proof is given that all functions definable in a certain affine linear typed lambda-calculus with iteration in all types are polynomial time computable. The proof provides explicit polynomial bounds that can easily be…
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…
The theory of finite term algebras provides a natural framework to describe the semantics of functional languages. The ability to efficiently reason about term algebras is essential to automate program analysis and verification for…
This paper enriches preexisting satisfiability tests for unquantified languages, which in turn augment a fragment of Tarski's elementary algebra with unary real functions possessing a continuous first derivative. Two sorts of individual…
The synthesis problem asks to automatically generate, if it exists, an algorithm from a specification of correct input-output pairs. In this paper, we consider the synthesis of computable functions of infinite words, for a classical Turing…
In previous work we describe a novel approach to dependent typing based on a multivalued term language. In this technical report we formalise the runtime, a kind of operational semantics, for that language. We describe a fairly…
The outcomes of this paper are twofold. Implicit complexity. We provide an implicit characterization of polynomial time computation in terms of ordinary differential equations: we characterize the class PTIME of languages computable in…
We propose a call-by-value lambda calculus extended with a new construct inspired by abductive inference and motivated by the programming idioms of machine learning. Although syntactically simple the abductive construct has a complex and…
Bidirectional typechecking, in which terms either synthesize a type or are checked against a known type, has become popular for its applicability to a variety of type systems, its error reporting, and its ease of implementation. Following…
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…
We show that a partial-correctness assertion about an iterative program is provable in Hoare Logic iffit is provable in standard second-order logic with comprehension restricted to first-order predicates. This equivalence was claimed twice…
This work deals with the definability problem by quantifier-free first-order formulas over a finite algebraic structure. We show the problem to be coNP-complete and present two decision algorithms based on a semantical characterization of…
Functors with an instance of the Traversable type class can be thought of as data structures which permit a traversal of their elements. This has been made precise by the correspondence between traversable functors and finitary containers…
We present gradual type theory, a logic and type theory for call-by-name gradual typing. We define the central constructions of gradual typing (the dynamic type, type casts and type error) in a novel way, by universal properties relative to…