arXiv subjects

Johannes K. Fichte

Publications and source records attributed to Johannes K. Fichte.

27 records · Page 2Linked to original sources

arXiv2020

Towards Faster Reasoners By Using Transparent Huge Pages

Various state-of-the-art automated reasoning (AR) tools are widely used as backend tools in research of knowledge representation and reasoning as well as in industrial applications. In testing and verification, those tools often run continuously or nightly. In this work, we present an approach to reduce the runtime of AR tools by 10% on average and up to 20% for long running tasks. Our improvement addresses the high memory usage that comes with the data structures used in AR tools, which are based on conflict driven no-good learning. We establish a general way to enable faster memory access by using the memory cache line of modern hardware more effectively. Therefore, we extend the standard C library (glibc) by dynamically allowing to use a memory management feature called huge pages. Huge pages allow to reduce the overhead that is required to translate memory addresses between the virtual memory of the operating system and the physical memory of the hardware. In that way, we can reduce runtime, costs, and energy consumption of AR tools and applications with similar memory access patterns simply by linking the tool against this new glibc library when compiling it. In every day industrial applications this easily allows to be more eco-friendly in computation. To back up the claimed speed-up, we present experimental results for tools that are commonly used in the AR community, including the domains ASP, BMC, MaxSAT, SAT, and SMT.

cs.LO↗

arXiv2019

Inconsistency Proofs for ASP: The ASP-DRUPE Format

Answer Set Programming (ASP) solvers are highly-tuned and complex procedures that implicitly solve the consistency problem, i.e., deciding whether a logic program admits an answer set. Verifying whether a claimed answer set is formally a correct answer set of the program can be decided in polynomial time for (normal) programs. However, it is far from immediate to verify whether a program that is claimed to be inconsistent, indeed does not admit any answer sets. In this paper, we address this problem and develop the new proof format ASP-DRUPE for propositional, disjunctive logic programs, including weight and choice rules. ASP-DRUPE is based on the Reverse Unit Propagation (RUP) format designed for Boolean satisfiability. We establish correctness of ASP-DRUPE and discuss how to integrate it into modern ASP solvers. Later, we provide an implementation of ASP-DRUPE into the wasp solver for normal logic programs. This work is under consideration for acceptance in TPLP.

cs.LO↗

arXiv2019

Treewidth and Counting Projected Answer Sets

In this paper, we introduce novel algorithms to solve projected answer set counting (#PAs). #PAs asks to count the number of answer sets with respect to a given set of projected atoms, where multiple answer sets that are identical when restricted to the projected atoms count as only one projected answer set. Our algorithms exploit small treewidth of the primal graph of the input instance by dynamic programming (DP). We establish a new algorithm for head-cycle-free (HCF) programs and lift very recent results from projected model counting to #PAs when the input is restricted to HCF programs. Further, we show how established DP algorithms for tight, normal, and disjunctive answer set programs can be extended to solve #PAs. Our algorithms run in polynomial time while requiring double exponential time in the treewidth for tight, normal, and HCF programs, and triple exponential time for disjunctive programs. Finally, we take the exponential time hypothesis (ETH) into account and establish lower bounds of bounded treewidth algorithms for #PAs. Under ETH, one cannot significantly improve our obtained worst-case runtimes.

cs.CC↗

arXiv2018

Counting Complexity for Reasoning in Abstract Argumentation

In this paper, we consider counting and projected model counting of extensions in abstract argumentation for various semantics. When asking for projected counts we are interested in counting the number of extensions of a given argumentation framework while multiple extensions that are identical when restricted to the projected arguments count as only one projected extension. We establish classical complexity results and parameterized complexity results when the problems are parameterized by treewidth of the undirected argumentation graph. To obtain upper bounds for counting projected extensions, we introduce novel algorithms that exploit small treewidth of the undirected argumentation graph of the input instance by dynamic programming (DP). Our algorithms run in time double or triple exponential in the treewidth depending on the considered semantics. Finally, we take the exponential time hypothesis (ETH) into account and establish lower bounds of bounded treewidth algorithms for counting extensions and projected extension.

cs.AI↗

arXiv2018

Exploiting Treewidth for Projected Model Counting and its Limits

In this paper, we introduce a novel algorithm to solve projected model counting (PMC). PMC asks to count solutions of a Boolean formula with respect to a given set of projected variables, where multiple solutions that are identical when restricted to the projected variables count as only one solution. Our algorithm exploits small treewidth of the primal graph of the input instance. It runs in time $O({2^{2^{k+4}} n^2})$ where k is the treewidth and n is the input size of the instance. In other words, we obtain that the problem PMC is fixed-parameter tractable when parameterized by treewidth. Further, we take the exponential time hypothesis (ETH) into consideration and establish lower bounds of bounded treewidth algorithms for PMC, yielding asymptotically tight runtime bounds of our algorithm.

cs.AI↗

arXiv2017

Default Logic and Bounded Treewidth

In this paper, we study Reiter's propositional default logic when the treewidth of a certain graph representation (semi-primal graph) of the input theory is bounded. We establish a dynamic programming algorithm on tree decompositions that decides whether a theory has a consistent stable extension (Ext). Our algorithm can even be used to enumerate all generating defaults (ExtEnum) that lead to stable extensions. We show that our algorithm decides Ext in linear time in the input theory and triple exponential time in the treewidth (so-called fixed-parameter linear algorithm). Further, our algorithm solves ExtEnum with a pre-computation step that is linear in the input theory and triple exponential in the treewidth followed by a linear delay to output solutions.

cs.AI↗

arXiv2017

DynASP2.5: Dynamic Programming on Tree Decompositions in Action

A vibrant theoretical research area are efficient exact parameterized algorithms. Very recent solving competitions such as the PACE challenge show that there is also increasing practical interest in the parameterized algorithms community. An important research question is whether dedicated parameterized exact algorithms exhibit certain practical relevance and one can even beat well-established problem solvers. We consider the logic-based declarative modeling language and problem solving framework Answer Set Programming (ASP). State-of-the-art ASP solvers rely considerably on Sat-based algorithms. An ASP solver (DynASP2), which is based on a classical dynamic programming on tree decompositions, has been published very recently. Unfortunately, DynASP2 can outperform modern ASP solvers on programs of small treewidth only if the question of interest is to count the number of solutions. In this paper, we describe underlying concepts of our new implementation (DynASP2.5) that shows competitive behavior to state-of-the-art ASP solvers even for finding just one solution when solving problems as the Steiner tree problem that have been modeled in ASP on graphs with low treewidth. Our implementation is based on a novel approach that we call multi-pass dynamic programming (M-DPSINC).

cs.LO↗

arXiv2016

Strong Backdoors for Default Logic

In this paper, we introduce a notion of backdoors to Reiter's propositional default logic and study structural properties of it. Also we consider the problems of backdoor detection (parameterised by the solution size) as well as backdoor evaluation (parameterised by the size of the given backdoor), for various kinds of target classes (cnf, horn, krom, monotone, identity). We show that backdoor detection is fixed-parameter tractable for the considered target classes, and backdoor evaluation is either fixed-parameter tractable, in para-DP2 , or in para-NP, depending on the target class.

cs.LO↗

arXiv2015

Dual-normal Logic Programs - the Forgotten Class

Disjunctive Answer Set Programming is a powerful declarative programming paradigm with complexity beyond NP. Identifying classes of programs for which the consistency problem is in NP is of interest from the theoretical standpoint and can potentially lead to improvements in the design of answer set programming solvers. One of such classes consists of dual-normal programs, where the number of positive body atoms in proper rules is at most one. Unlike other classes of programs, dual-normal programs have received little attention so far. In this paper we study this class. We relate dual-normal programs to propositional theories and to normal programs by presenting several inter-translations. With the translation from dual-normal to normal programs at hand, we introduce the novel class of body-cycle free programs, which are in many respects dual to head-cycle free programs. We establish the expressive power of dual-normal programs in terms of SE- and UE-models, and compare them to normal programs. We also discuss the complexity of deciding whether dual-normal programs are strongly and uniformly equivalent.

cs.CC↗