Related papers: A Proof Synthesis Algorithm for a Mathematical Ver…
The continuous functional calculus is perhaps the most fundamental construction in the theory of operator algebras, especially $C^{*}$-algebras. Here we document our formalization of the continuous functional calculus in Lean, which…
A method is presented for using the consistent part of inconsistent axiomatic systems.
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
This paper shows how proof nets can be used to formalize the notion of ``incomplete dependency'' used in psycholinguistic theories of the unacceptability of center-embedded constructions. Such theories of human language processing can…
In the last few years appeared pedagogical propositional natural deduction systems. In these systems, one must satisfy the pedagogical constraint: the user must give an example of any introduced notion. First we expose the reasons of such a…
In this paper we study possibilities of using hierarchical reasoning, symbol elimination and model generation for the verification of parametric systems, where the parameters can be constants or functions. Our goal is to automatically…
Essential tasks for the verification of probabilistic programs include bounding expected outcomes and proving termination in finite expected runtime. We contribute a simple yet effective inductive synthesis approach for proving such…
We define a proof system for exceptions which is close to the syntax for exceptions, in the sense that the exceptions do not appear explicitly in the type of any expression. This proof system is sound with respect to the intended…
General purpose correct-by-construction synthesis methods are limited to systems with low dimensionality or simple specifications. In this work we consider highly symmetrical counting problems and exploit the symmetry to synthesize provably…
We identify a decidable synthesis problem for a class of programs of unbounded size with conditionals and iteration that work over infinite data domains. The programs in our class use uninterpreted functions and relations, and abide by a…
This thesis embarks on a comprehensive exploration of formal computational models that underlie typed programming languages. We focus on programming calculi, both functional (sequential) and concurrent, as they provide a compelling rigorous…
Verifying partial (i.e., termination-insensitive) equivalence of programs has significant practical applications in software development and education. Conventional equivalence verifiers typically rely on a combination of given relational…
A grammar logic refers to an extension to the multi-modal logic K in which the modal axioms are generated from a formal grammar. We consider a proof theory, in nested sequent calculus, of grammar logics with converse, i.e., every modal…
In this paper, we investigate the proof complexity of a wide range of substructural systems. For any proof system $\mathbf{P}$ at least as strong as Full Lambek calculus, $\mathbf{FL}$, and polynomially simulated by the extended Frege…
In this paper, a library-based synthesis methodology for reversible circuits is proposed where a reversible specification is considered as a permutation comprising a set of cycles. To this end, a pre-synthesis optimization step is…
We present a new approach to proving non-termination of non-deterministic integer programs. Our technique is rather simple but efficient. It relies on a purely syntactic reversal of the program's transition system followed by a…
A term calculus for the proofs in multiplicative-additive linear logic is introduced and motivated as a programming language for channel based concurrency. The term calculus is proved complete for a semantics in linearly distributive…
The classical technique for proving termination of a generic sequential computer program involves the synthesis of a ranking function for each loop of the program. Linear ranking functions are particularly interesting because many…
We provide a sound and complete proof system for an extension of Kleene's ternary logic to predicates. The concept of theory is extended with, for each function symbol, a formula that specifies when the function is defined. The notion of…
Sums-of-squares formulas over the integers have been studied extensively using their equivalence to consistently signed intercalate matrices. This representation, combined with combinatorial arguments, has been used to produce…