Related papers: Non-termination using Regular Languages
Deep neural networks for natural language processing are fragile in the face of adversarial examples -- small input perturbations, like synonym substitution or word duplication, which cause a neural network to change its prediction. We…
Recurrent neural networks are a widely used class of neural architectures. They have, however, two shortcomings. First, it is difficult to understand what exactly they learn. Second, they tend to work poorly on sequences requiring long-term…
We propose TOPL automata as a new method for runtime verification of systems with unbounded resource generation. Paradigmatic such systems are object-oriented programs which can dynamically generate an unbounded number of fresh object…
Dynamic logic is a modal logic for reasoning about programs. A cyclic proof system is a proof system that allows proofs containing cycles and is an alternative to a proof system containing (co-)induction. This paper introduces a sequent…
This thesis is concerned with investigations into the "complexity of term rewriting systems". Moreover the majority of the presented work deals with the "automation" of such a complexity analysis. The aim of this introduction is to present…
In this article we investigate how a subterm pattern matching algorithm can be exploited to implement efficient term rewriting procedures. From the left-hand sides of the rewrite system we construct a set automaton, which can be used to…
We consider some questions about formal languages that arise when inverses of letters, words and languages are defined. The reduced representation of a language over the free monoid is its unique equivalent representation in the free group.…
Rewriting Induction (RI) is a formal system in term rewriting to establish program equivalence. The recently defined Bounded RI for higher-order Logically Constrained Term Rewriting Systems (LCSTRSs) yields a convenient proof system for…
In this work we prove decidability of the model-checking problem for safe recursion schemes against properties defined by alternating B-automata. We then exploit this result to show how to compute downward closures of languages of finite…
We present a new kind of nontermination argument for linear lasso programs, called geometric nontermination argument. A geometric nontermination argument is a finite representation of an infinite execution of the form $(\vec{x} +…
In various models of one-way pushdown automata, the explicit use of two designated endmarkers on a read-once input tape has proven to be extremely useful for making a conscious, final decision on the acceptance/rejection of each input word…
Sequence theories are an extension of theories of strings with an infinite alphabet of letters, together with a corresponding alphabet theory (e.g. linear integer arithmetic). Sequences are natural abstractions of extendable arrays, which…
This paper proposes a data tree-rewriting framework for modeling evolving documents. The framework is close to Guarded Active XML, a platform used for handling XML repositories evolving through web services. We focus on automatic…
We introduce a general theory of quantitative and metric rewriting systems, namely systems with a rewriting relation enriched over quantales modelling abstract quantities. We develop theories of abstract and term-based systems, refining…
We consider formal verification of recursive programs with resource consumption. We introduce prefix replacement systems with non-negative integer counters which can be incremented and reset to zero as a formal model for such programs. In…
We model collapsible and ordered pushdown systems with term rewriting, by encoding higher-order stacks and multiple stacks into trees. We show a uniform inverse preservation of recognizability result for the resulting class of term…
Our goal is to study the feasibility of porting termination analysis techniques developed for one programming paradigm to another paradigm. In this paper, we show how to adapt termination analysis techniques based on polynomial…
We present decidability results for termination of classes of term rewriting systems modulo permutative theories. Termination and innermost termination modulo permutative theories are shown to be decidable for term rewrite systems (TRS)…
We prove a kind of a pumping lemma for languages accepted by one-register alternating finite-memory automata. As a corollary, we obtain that the set of lengths of words in such languages is semi-linear.
Justification theory is an abstract unifying formalism that captures semantics of various non-monotonic logics. One intriguing problem that has received significant attention is the consistency problem: under which conditions are…