Related papers: On First-order Cons-free Term Rewriting and PTIME
Constructor rewriting systems are said to be cons-free if, roughly, constructor terms in the right-hand sides of rules are subterms of the left-hand sides; the computational intuition is that rules cannot build new data structures. In…
Constructor rewriting systems are said to be cons-free if, roughly, constructor terms in the right-hand sides of rules are subterms of constructor terms in the left-hand side; the computational intuition is that rules cannot build new data…
We propose to consider non confluence with respect to implicit complexity. We come back to some well known classes of first-order functional program, for which we have a characterization of their intentional properties, namely the class of…
Constructor rewriting systems are said to be cons-free if any constructor term occurring in the rhs of a rule must be a subterm of the lhs of the rule. Roughly, such systems cannot build new data structures during their evaluation. In…
This paper discusses the method of formative rules for first-order term rewriting, which was previously defined for a higher-order setting. Dual to the well-known usable rules, formative rules allow dropping some of the term constraints…
Adopting former term rewriting characterisations of polytime and exponential-time computable functions, we introduce a new reduction order, the Path Order for ETIME (POE* for short), that is sound and complete for ETIME computable…
In this short paper, we consider a form of higher-order rewriting with a call-by-value evaluation strategy so as to model call-by-value programs. We briefly present a cost-size semantics to call-by-value rewriting: a class of algebraic…
The central open question in Descriptive Complexity is whether there is a logic that characterizes deterministic polynomial time (PTIME) on relational structures. Towards this goal, we define a logic that is obtained from first-order logic…
The class of type-two basic feasible functionals ($\mathtt{BFF}_2$) is the analogue of $\mathtt{FP}$ (polynomial time functions) for type-2 functionals, that is, functionals that can take (first-order) functions as arguments.…
Qualification has been recently introduced as a generalization of uncertainty in the field of Logic Programming. In this report we investigate a more expressive language for First-Order Functional Logic Programming with Constraints and…
The search for a logic capturing PTIME is a long standing open problem in finite model theory. One of the most promising candidate logics for this is Choiceless Polynomial Time with counting (CPT). Abstractly speaking, CPT is an…
In deduction modulo, a theory is not represented by a set of axioms but by a congruence on propositions modulo which the inference rules of standard deductive systems---such as for instance natural deduction---are applied. Therefore, the…
Proof terms are syntactic expressions that represent computations in term rewriting. They were introduced by Meseguer and exploited by van Oostrom and de Vrijer to study equivalence of reductions in (left-linear) first-order term rewriting…
In this paper we deal with verification of safety properties of term-rewriting systems. The verification problem is translated to a purely logical problem of finding a finite countermodel for a first-order formula, which further resolved by…
Proof terms in term rewriting are a representation means for reduction sequences, and more in general for contraction activity, allowing to distinguish e.g simultaneous from sequential reduction. Proof terms for finitary, first-order,…
Traditional automated theorem provers for first-order logic depend on speed-optimized search and many handcrafted heuristics that are designed to work best over a wide range of domains. Machine learning approaches in literature either…
Various feature descriptions are being employed in logic programming languages and constrained-based grammar formalisms. The common notational primitive of these descriptions are functional attributes called features. The descriptions…
We prove a characterization of first-order string-to-string transduction via $\lambda$-terms typed in non-commutative affine logic that compute with Church encoding, extending the analogous known characterization of star-free languages. We…
We present a first-order theorem proving framework for establishing the correctness of functional programs implementing sorting algorithms with recursive data structures. We formalize the semantics of recursive programs in many-sorted…
In this paper we study the complexity of the problems: given a loop, described by linear constraints over a finite set of variables, is there a linear or lexicographical-linear ranking function for this loop? While existence of such…