# Computer Science - Logic in Computer Science Publications (50)

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## Computer Science - Logic in Computer Science Publications

Congruence closure procedures are used extensively in automated reasoning and are a core component of most satisfiability modulo theories solvers. However, no known congruence closure algorithms can support any of the expressive logics based on intensional type theory (ITT), which form the basis of many interactive theorem provers. The main source of expressiveness in these logics is dependent types, and yet existing congruence closure procedures found in interactive theorem provers based on ITT do not handle dependent types at all and only work on the simply-typed subsets of the logics. Read More

There is still a lot of confusion about "optimal" sharing in the lambda calculus, and its actual efficiency. In this article, we shall try to clarify some of these issues. Read More

We introduce a system of monadic affine sized types, which substantially generalise usual sized types, and allows this way to capture probabilistic higher-order programs which terminate almost surely. Going beyond plain, strong normalisation without losing soundness turns out to be a hard task, which cannot be accomplished without a richer, quantitative notion of types, but also without imposing some affinity constraints. The proposed type system is powerful enough to type classic examples of probabilistically terminating programs such as random walks. Read More

Let A be an idempotent algebra on a finite domain. We combine results of Chen and Zhuk to argue that if Inv(A) satisfies the polynomially generated powers property (PGP), then QCSP(Inv(A)) is in NP. We then use the result of Zhuk to prove a converse, that if Inv(A) satisfies the exponentially generated powers property (EGP), then QCSP(Inv(A)) is co-NP-hard. Read More

We propose a generalization of first-order logic originating in a neglected work by C.C. Chang: a natural and generic correspondence language for any types of structures which can be recast as Set-coalgebras. Read More

We introduce a logic, called LT, to express properties of transductions, i.e. binary relations from input to output (finite) words. Read More

LogicWeb has traditionally lacked devices for dealing with intractable queries. We address this limitation by adopting length-bounded inference, a form of approximate reasoning. A {\it length-bounded} inference is of the form $prov(P,G,n)$ which is a success if a query $G$ can be proved from the web page $P$ {\it within} $n$ proof steps. Read More

Automatic verification deals with the validation by means of computers of correctness certificates. The related tools, usually called proof assistants or interactive provers, provide an interactive environment for the creation of formal certificates whose correctness can be assessed in a purely automatic way. Such systems have applications both in mathematics, where certificates are proofs of theorems, and in computer science, where certificates testify the correctness of a given software with respect to its specification. Read More

SRAM-based FPGAs are increasingly popular in the aerospace industry due to their field programmability and low cost. However, they suffer from cosmic radiation induced Single Event Upsets (SEUs). In safety-critical applications, the dependability of the design is a prime concern since failures may have catastrophic consequences. Read More

**Affiliations:**

^{1}Universidad Complutense de Madrid

This paper is a tutorial introducing the underlying technology and the use of the tool Liquid Haskell, a type-checker for the functional language Haskell that can help programmers to verify non-trivial properties of their programs with a low effort. The first sections introduce the technology of Liquid Types by explaining its principles and summarizing how its type inference algorithm manages to prove properties. The remaining sections present a selection of Haskell examples and show the kind of properties that can be proved with the system. Read More

We prove that the set of all solutions for twisted word equations with regular constraints is an EDT0L language and can be computed in PSPACE. It follows that the set of solutions to equations with rational constraints in a context-free group (= finitely generated virtually free group) in reduced normal forms is EDT0L. We can also decide (in PSPACE) whether or not the solution set is finite, which was an open problem. Read More

In this paper we propose augmented interval Markov chains (AIMCs): a generalisation of the familiar interval Markov chains (IMCs) where uncertain transition probabilities are in addition allowed to depend on one another. This new model preserves the flexibility afforded by IMCs for describing stochastic systems where the parameters are unclear, for example due to measurement error, but also allows us to specify transitions with probabilities known to be identical, thereby lending further expressivity. The focus of this paper is reachability in AIMCs. Read More

We consider the problems of liveness verification and liveness synthesis for recursive programs. The liveness verification problem (LVP) is to decide whether a given omega-context-free language is contained in a given omega-regular language. The liveness synthesis problem (LSP) is to compute a strategy so that a given omega-context-free game, when played along the strategy, is guaranteed to derive a word in a given omega-regular language. Read More

We study the size and the complexity of computing finite state automata (FSA) representing and approximating the downward and the upward closure of Petri net languages with coverability as the acceptance condition. We show how to construct an FSA recognizing the upward closure of a Petri net language in doubly-exponential time, and therefore the size is at most doubly exponential. For downward closures, we prove that the size of the minimal automata can be non-primitive recursive. Read More

We introduce a sequent calculus with a simple restriction of Lambek's product rules that precisely captures the classical Tamari order, i.e., the partial order on fully-bracketed words (equivalently, binary trees) induced by a semi-associative law (equivalently, tree rotation). Read More

Decidability of the determinization problem for weighted automata over the semiring $(\mathbb{Z} \cup {-\infty}, \max, +)$, WA for short, is a long-standing open question. We propose two ways of approaching it by constraining the search space of deterministic WA: k-delay and r-regret. A WA N is k-delay determinizable if there exists a deterministic automaton D that defines the same function as N and for all words {\alpha} in the language of N, the accepting run of D on {\alpha} is always at most k-away from a maximal accepting run of N on {\alpha}. Read More

A devil's advocate is one who argues against a claim, not as a committed opponent but in order to determine the validity of the claim. We are interested in a devil's advocate that argues against termination of a program. He does so by producing a maleficent program that can cause the non-termination of the original program. Read More

First-order logic (FO) over words is shown to be equiexpressive with FO equipped with a restricted set of numerical predicates, namely the order, a binary predicate MSB$_0$, and the finite-degree predicates: FO[Arb] = FO[<, MSB$_0$, Fin]. The Crane Beach Property (CBP), introduced more than a decade ago, is true of a logic if all the expressible languages admitting a neutral letter are regular. Although it is known that FO[Arb] does not have the CBP, it is shown here that the (strong form of the) CBP holds for both FO[<, Fin] and FO[<, MSB$_0$]. Read More

Constraint Handling Rules (CHR) is both an effective concurrent declarative constraint-based programming language and a versatile computational formalism. While conceptually simple, CHR is distinguished by a remarkable combination of desirable features: - semantic foundation in classical and linear logic, - effective and efficient sequential and parallel execution model - guaranteed properties like the anytime online algorithm properties - powerful analysis methods for deciding essential program properties. This overview of CHR research and applications is by no complete. Read More

This paper is concerned with rule-based programs that go wrong. The unwanted behavior of rule applications is non-termination or failure of a computation. We propose a static program analysis of the non-termination problem for recursion in the Constraint Handling Rules (CHR) language. Read More

There are two well known types of algorithms for solving CSPs: local propagation and generating a basis of the solution space. For several years the focus of the CSP research has been on `hybrid' algorithms that somehow combine the two approaches. In this paper we present a new method of such hybridization that allows us to solve certain CSPs that has been out of reach for a quite a while. Read More

We give a model of dependent type theory with one univalent universe and propositional truncation interpreting a type as a stack, generalising the groupoid model of type theory. As an application, we show that countable choice cannot be proved in dependent type theory with one univalent universe and propositional truncation. Read More

Higher-order probabilistic programming languages allow programmers to write sophisticated models in machine learning and statistics in a succinct and structured way, but step outside the standard measure-theoretic formalization of probability theory. Programs may use both higher-order functions and continuous distributions, or even define a probability distribution on functions. But standard probability theory cannot support higher-order functions, that is, the category of measurable spaces is not cartesian closed. Read More

Energy-parity objectives combine $\omega$-regular with quantitative objectives of reward MDPs. The controller needs to avoid to run out of energy while satisfying a parity objective. We refute the common belief that, if an energy-parity objective holds almost-surely, then this can be realised by some finite memory strategy. Read More

We propose a graph-based process calculus for modelling and reasoning about wireless networks with local broadcast. To study the behavioural theory of wireless networks, we develop both a reduction semantics and a labelled transition semantics. Then we derive weak barbed congruence and weak bisimilarity based on these semantics, respectively. Read More

This paper studies dynamic complexity under definable change operations in the DynFO framework by Patnaik and Immerman. It is shown that for changes definable by parameter-free first-order formulas, all (uniform) $AC^1$ queries can be maintained by first-order dynamic programs. Furthermore, many maintenance results for single-tuple changes are extended to more powerful change operations: (1) The reachability query for undirected graphs is first-order maintainable under single tuple changes and first-order defined insertions, likewise the reachability query for directed acyclic graphs under quantifier-free insertions. Read More

We study properties of classes of closure operators and closure systems parameterized by systems of isotone Galois connections. The parameterizations express stronger requirements on idempotency and monotony conditions of closure operators. The present approach extends previous approaches to fuzzy closure operators which appeared in analysis of object-attribute data with graded attributes and reasoning with if-then rules in graded setting and is also related to analogous results developed in linear temporal logic. Read More

Stable event structures, and their duality with prime algebraic domains (arising as partial orders of configurations), are a landmark of concurrency theory, providing a clear characterisation of causality in computations. They have been used for defining a concurrent semantics of several formalisms, from Petri nets to linear graph rewriting systems, which in turn lay at the basis of many visual frameworks. Stability however is restrictive for dealing with formalisms where a computational step can merge parts of the state, like graph rewriting systems with non-linear rules, which are needed to cover some relevant applications (such as the graphical encoding of calculi with name passing). Read More

Many algorithms for satisfiability checking are based either on resolution or on Ordered Binary Decision Diagrams (OBDDs). Atserias, Kolaitis and Vardi proposed a proof system based on OBDDs. In this study we consider a restriction of their proof system corresponding to the combination of Axiom and Join rules on the one hand and resolution on the other hand. Read More

We extend the framework by Kawamura and Cook for investigating computational complexity for operators occurring in analysis. This model is based on second-order complexity theory for functions on the Baire space, which is lifted to metric spaces by means of representations. Time is measured in terms of the length of the input encodings and the required output precision. Read More

The \emph{Orbit Problem} consists of determining, given a linear transformation $A$ on $\mathbb{Q}^d$, together with vectors $x$ and $y$, whether the orbit of $x$ under repeated applications of $A$ can ever reach $y$. This problem was famously shown to be decidable by Kannan and Lipton in the 1980s. In this paper, we are concerned with the problem of synthesising suitable \emph{invariants} $\mathcal{P} \subseteq \mathbb{R}^d$, \emph{i. Read More

Knapik et al. introduced the safety restriction which constrains both the types and syntax of the production rules defining a higher-order recursion scheme. This restriction gives rise to an equi-expressivity result between order-n pushdown automata and order-n safe recursion schemes, when such devices are used as tree generators. Read More

This paper presents the notion of AND-OR reduction, which reduces a WF net to a smaller net by iteratively contracting certain well-formed subnets into single nodes until no more such contractions are possible. This reduction can reveal the hierarchical structure of a WF net, and since it preserves certain semantical properties such as soundness, it can help with analysing and understanding why a WF net is sound or not. The reduction can also be used to verify if a WF net is an AND-OR net. Read More

Several variants of linear logic have been proposed to characterize complexity classes in the proofs-as-programs correspondence. Light linear logic (LLL) ensures a polynomial bound on reduction time, and characterizes in this way polynomial time (Ptime). In this paper we study the complexity of linear logic proof-nets and propose three semantic criteria based on context semantics: stratification, dependence control and nesting. Read More

We prove that the semantics of intuitionistic linear logic in vector spaces which uses cofree coalgebras to model the exponential is a model of differential linear logic. Thus, in this semantics, proof denotations have natural derivatives. We give several examples of these derivatives. Read More

This paper proves the approximate intermediate value theorem, constructively and from notably weak hypotheses: from pointwise rather than uniform continuity, without assuming that reals are presented with rational approximants, and without using countable choice. The theorem is that if a pointwise continuous function has both a negative and a positive value, then it has values arbitrarily close to 0. The proof builds on the usual classical proof by bisection, which repeatedly selects the left or right half of an interval; the algorithm here selects an interval of half the size in a continuous way, interpolating between those two possibilities. Read More

We present a new metric temporal logic HornMTL over dense time and its datalog extension datalogMTL. The use of datalogMTL is demonstrated in the context of ontology-based data access over meteorological data. We show decidability of answering ontology-mediated queries for a practically relevant non-recursive fragment of datalogMTL. Read More

We revisit the notion of probably approximately correct implication bases from the literature and present a first formulation in the language of formal concept analysis, with the goal to investigate whether such bases represent a suitable substitute for exact implication bases in practical use-cases. To this end, we quantitatively examine the behavior of probably approximately correct implication bases on artificial and real-world data sets and compare their precision and recall with respect to their corresponding exact implication bases. Using a small example, we also provide qualitative insight that implications from probably approximately correct bases can still represent meaningful knowledge from a given data set. Read More

We study rewritability of monadic disjunctive Datalog programs, (the complements of) MMSNP sentences, and ontology-mediated queries (OMQs) based on expressive description logics of the ALC family and on conjunctive queries. We show that rewritability into FO and into monadic Datalog (MDLog) are decidable, and that rewritability into Datalog is decidable when the original query satisfies a certain condition related to equality. We establish 2NExpTime-completeness for all studied problems except rewritability into MDLog for which there remains a gap between 2NExpTime and 3ExpTime. Read More

**Affiliations:**

^{1}Radboud University,

^{2}Oxford University,

^{3}Aalborg University

In this paper, W*-algebras are presented as canonical colimits of diagrams of matrix algebras and completely positive maps. In other words, matrix algebras are dense in W*-algebras. Read More

**Affiliations:**

^{1}University of Oxford

We investigate notions of ambiguity and partial information in categorical distributional models of natural language. Probabilistic ambiguity has previously been studied using Selinger's CPM construction. This construction works well for models built upon vector spaces, as has been shown in quantum computational applications. Read More

Techniques from higher categories and higher-dimensional rewriting are becoming increasingly important for understanding the finer, computational properties of higher algebraic theories that arise, among other fields, in quantum computation. These theories have often the property of containing simpler sub-theories, whose interaction is regulated in a limited number of ways, which reveals a topological substrate when pictured by string diagrams. By exploring the double nature of computads as presentations of higher algebraic theories, and combinatorial descriptions of "directed spaces", we develop a basic language of directed topology for the compositional study of algebraic theories. Read More

**Affiliations:**

^{1}University of Oxford

Recent work by Abramsky and Brandenburger used sheaf theory to give a mathematical formulation of non-locality and contextuality. By adopting this viewpoint, it has been possible to define cohomological obstructions to the existence of global sections. In the present work, we illustrate new insights into different aspects of this theory. Read More

**Affiliations:**

^{1}Nagoya University,

^{2}Nagoya University,

^{3}Nagoya University

In this paper, we show that the SR transformation, a computationally equivalent transformation proposed by Serbanuta and Rosu, is a sound structure-preserving transformation for weakly-left-linear deterministic conditional term rewriting systems. More precisely, we show that every weakly-left-linear deterministic conditional term rewriting system can be converted to an equivalent weakly-left-linear and ultra-weakly-left-linear deterministic conditional term rewriting system and prove that the SR transformation is sound for weakly-left-linear and ultra-weakly-left-linear deterministic conditional term rewriting systems. Here, soundness for a conditional term rewriting system means that reduction of the transformed unconditional term rewriting system creates no undesired reduction sequence for the conditional system. Read More

**Affiliations:**

^{1}Nagoya University,

^{2}Nagoya University,

^{3}Nagoya University

A parameterised Boolean equation system (PBES) is a set of equations that defines sets as the least and/or greatest fixed-points that satisfy the equations. This system is regarded as a declarative program defining functions that take a datum and returns a Boolean value. The membership problem of PBESs is a problem to decide whether a given element is in the defined set or not, which corresponds to an execution of the program. Read More

**Affiliations:**

^{1}UAS Technikum Wien

Conditional term rewriting is an intuitive yet complex extension of term rewriting. In order to benefit from the simpler framework of unconditional rewriting, transformations have been defined to eliminate the conditions of conditional term rewrite systems. Recent results provide confluence criteria for conditional term rewrite systems via transformations, yet they are restricted to CTRSs with certain syntactic properties like weak left-linearity. Read More

**Affiliations:**

^{1}Gunma University

The Church-Rosser theorem in the type-free lambda-calculus is well investigated both for beta-equality and beta-reduction. We provide a new proof of the theorem for beta-equality with no use of parallel reductions, but simply with Takahashi's translation (Gross-Knuth strategy). Based on this, upper bounds for reduction sequences on the theorem are obtained as the fourth level of the Grzegorczyk hierarchy. Read More

**Affiliations:**

^{1}University of Wuerzburg,

^{2}University of Wuerzburg,

^{3}University of Wuerzburg,

^{4}University of Wuerzburg

System relevant embedded software needs to be reliable and, therefore, well tested, especially for aerospace systems. A common technique to verify programs is the analysis of their abstract syntax tree (AST). Tree structures can be elegantly analyzed with the logic programming language Prolog. Read More

**Affiliations:**

^{1}Heinrich-Heine Universität Düsseldorf,

^{2}Heinrich-Heine Universität Düsseldorf

We present a CLP(FD)-based constraint solver able to deal with unbounded domains. It is based on constraint propagation, resorting to enumeration if all other methods fail. An important aspect is detecting when enumeration was complete and if this has an impact on the soundness of the result. Read More

**Affiliations:**

^{1}University of Halle,

^{2}University of Halle

OpenRuleBench is a large benchmark suite for rule engines, which includes deductive databases. We previously proposed a translation of Datalog to C++ based on a method that "pushes" derived tuples immediately to places where they are used. In this paper, we report performance results of various implementation variants of this method compared to XSB, YAP and DLV. Read More