We call any consistent and sufficiently powerful formal theory that enables to algorithmically verify whether a text is a proof algorithmically verifiable mathematics (av-mathematics). We study the fundamental question whether nondeterminism is ...

• This article deals with the question whether nondeterminism is more
• powerful than determinism and tries to give more arguments for the positive
• answer and also outlines why solving this problem is so hard.

During the last few years, BDD-based SMT solvers proved to be competitive in deciding satisfiability of quantified bit-vector formulas. However, these solvers usually do not perform well on input formulas with complicated arithmetic. Hitherto, ...

We study the relation between the structure of algebraic and context-free subsets of a group G and that of a finite index subgroup H. Using these results, we prove that a kind of Fatou property, previously studied by Berstel and Sakarovitch in ...

System I is a proof language for a fragment of propositional logic where isomorphic propositions, such as A ∧ B and B ∧ A, or A ⇒ ( B ∧ C ) and ( A ⇒ B ) ∧ ( A ⇒ C ) are made equal. System I enjoys the strong normalization property. This is ...

We continue our investigation aimed at spotting small fragments of Set Theory (in this paper, sublanguages of Boolean Set Theory) that might be of use in automated proof-checkers based on the set-theoretic formalism. Here we propose a method that ...

Unified Temporal Logic (UTL) combines all characteristics of traditional Linear Temporal Logic (LTL) and Propositional Projection Temporal Logic (PPTL). It can be used to describe full regular and omega-regular properties, which are ...

Gödel's Dialectica interpretation was conceived as a tool to obtain the consistency of Heyting arithmetic in the 40s. In recent years, several proof theoretic transformations, based on Gödel's Dialectica interpretation, have been used ...

Following the Kronecker–Duval or D5 philosophy of dynamic evaluation in computer algebra, the dynamical proof method was brought into constructive algebra in order to obtain computational interpretations of the individual, concrete ...

Widespread use of string solvers in the formal analysis of string-heavy programs has led to a growing demand for more efficient and reliable techniques which can be applied in this context. Designing practical algorithms for the (...

The Vietoris space of a Stone space plays an important role in the coalgebraic approach to modal logic. When generalizing this to positive modal logic, there is a variety of relevant hyperspace constructions based on various topologies ...

• In section 2 we include all definitions and facts on Bishop spaces that are necessary to the rest of the paper.

We introduce the notion of a Bishop topological group i.e., a group X equipped with a Bishop topology of functions F such that the group operations of X are Bishop morphisms with respect to F. A closed subset in the neighborhood ...

The notion of clause set cycle abstracts a family of methods for automated inductive theorem proving based on the detection of cyclic dependencies between clause sets. By discerning the underlying logical features of clause set cycles, ...

We present, in outline, a constructive development of set theory in the style of A.P. Morse's classical counterpart [10]. Since the development is carried in a very precise formal language, it readily lends itself to computer-assisted ...

• A development of constructive set theory in Morse's formal language, which should facilitate both proof checking and program extraction from proofs.

We design a new preprocessing succinct non-interactive argument (SNARG) for rank-1 constraint satisfiability (R1CS) from holographic Interactive Oracle Proofs (IOPs). The protocol is secure in the random oracle model (ROM). We achieve ...

• A new holographic IOP for R1CS is proposed.
• A transformation form holographic ...

Generalized numberings are an extension of Ershov's notion of numbering, based on partial combinatory algebra (pca) instead of the natural numbers. We study various algebraic properties of generalized numberings, relating properties of ...

Catalytic P systems and purely catalytic P systems are among the first variants of membrane systems ever considered in this area. These variants of systems also feature some prominent computational complexity questions, and in ...

We present a family of avoidable formulas with reversal whose avoidability index is unbounded. We also complete the determination of the avoidability index of the formulas with reversal in the 3-avoidance basis.

Ripple Effect is a logic puzzle where the player has to fill numbers into empty cells in a rectangular grid. The grid is divided into rooms, and each room must contain consecutive integers starting from 1 to its size. Also, if two cells in the ...

• The copy complexity of a Horn formula equals the copy complexity of the corresponding system of constraints.

In this paper, we discuss the copy complexity of Horn formulas with respect to unit resolution. A Horn formula is a boolean formula in conjunctive normal form (CNF) with at most one positive literal per clause. Horn formulas find ...

Based on analogies between algebraic curves and graphs, Baker and Norine introduced divisorial gonality, a graph parameter for multigraphs related to treewidth, multigraph algorithms and number theory. Various equivalent definitions of ...