Results 1  10
of
17
New methods for 3SAT decision and worstcase analysis
 THEORETICAL COMPUTER SCIENCE
, 1999
"... We prove the worstcase upper bound 1:5045 n for the time complexity of 3SAT decision, where n is the number of variables in the input formula, introducing new methods for the analysis as well as new algorithmic techniques. We add new 2 and 3clauses, called "blocked clauses", generalizing the e ..."
Abstract

Cited by 66 (12 self)
 Add to MetaCart
We prove the worstcase upper bound 1:5045 n for the time complexity of 3SAT decision, where n is the number of variables in the input formula, introducing new methods for the analysis as well as new algorithmic techniques. We add new 2 and 3clauses, called "blocked clauses", generalizing the extension rule of "Extended Resolution." Our methods for estimating the size of trees lead to a refined measure of formula complexity of 3clausesets and can be applied also to arbitrary trees. Keywords: 3SAT, worstcase upper bounds, analysis of algorithms, Extended Resolution, blocked clauses, generalized autarkness. 1 Introduction In this paper we study the exponential part of time complexity for 3SAT decision and prove the worstcase upper bound 1:5044:: n for n the number of variables in the input formula, using new algorithmic methods as well as new methods for the analysis. These methods also deepen the already existing approaches in a systematically manner. The following results...
Grail: A C++ Library for Automata and Expressions
 JOURNAL OF SYMBOLIC COMPUTATION
, 1995
"... ..."
Index Set Splitting
 International Journal of Parallel Programming
, 1999
"... There are many algorithms for the spacetime mapping of nested loops. Some of them even make the optimal choices within their framework. We propose a preprocessing phase for algorithms in the polytope model, which extends the model and yields spacetime mappings whose schedule is, in some cases, ord ..."
Abstract

Cited by 10 (1 self)
 Add to MetaCart
There are many algorithms for the spacetime mapping of nested loops. Some of them even make the optimal choices within their framework. We propose a preprocessing phase for algorithms in the polytope model, which extends the model and yields spacetime mappings whose schedule is, in some cases, orders of magnitude faster. These are cases in which the dependence graph has small irregularities. The basic idea is to split the iteration domain of the loop nests into parts with a regular dependence structure and apply the existing spacetime mapping algorithms to these parts individually. This work is based on a seminal idea in the more limited context of loop parallelization at the code level. We elevate the idea to the model level (our model is the polytope model), which increases its applicability by providing a clearer and wider range of choices at an acceptable analysis cost. Index set splitting is one facet in the e ort to extend the power of the polytope model and to en...
3Coloring in time O(1.3446^n): a noMIS algorithm
, 1995
"... We consider worst case time bounds for NPcomplete problems including 3SAT, 3coloring, 3edgecoloring, and 3listcoloring. Our algorithms are based on a common generalization of these problems, called symbolsystem satisfiability or, briefly, SSS [1]. 3SAT is equivalent to (2,3)SSS while the ..."
Abstract

Cited by 9 (0 self)
 Add to MetaCart
We consider worst case time bounds for NPcomplete problems including 3SAT, 3coloring, 3edgecoloring, and 3listcoloring. Our algorithms are based on a common generalization of these problems, called symbolsystem satisfiability or, briefly, SSS [1]. 3SAT is equivalent to (2,3)SSS while the other problems above are special cases of (3,2)SSS; there is also a natural duality transformation from (a; b)SSS to (b; a)SSS. We give a fast algorithm for (3,2)SSS and use it to improve the time bounds for solving the other problems listed above. 1 Introduction There are many known NPcomplete problems including such important graph theoretic problems as coloring and independent sets. Unless P=NP, we know that no polynomial time algorithm for these problems can exist, but that does not obviate the need to solve them as efficiently as possible, indeed the fact that these problems are hard makes efficient algorithms for them especially important. We are interested in this paper in...
Physical programming: Tools for kindergarten children to author physical interactive environments
, 2003
"... StoryRooms is a childcentered ubiquitous computing environment (ubicomp) developed for young children to expresses stories. Physical programming is a set of tangible tools and user interaction metaphors for children to control the behaviors of embedded objects in StoryRooms. In this dissertation I ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
StoryRooms is a childcentered ubiquitous computing environment (ubicomp) developed for young children to expresses stories. Physical programming is a set of tangible tools and user interaction metaphors for children to control the behaviors of embedded objects in StoryRooms. In this dissertation I describe StoryRooms and physical programming, along with the two studies which showed that kindergarten students had the capacity to understand and use the physical programming approach to control the specialized StoryRooms.
Transition Diagram Systems and Normal Form Algorithms
, 1998
"... We investigate the complexity of a variety of normalform transformations for transition diagram systems, which are a parsing view of extended contextfree grammars. A transition diagram system is a finite collection of finitestate machines each of which is labeled with a unique nonterminal symbol. ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
We investigate the complexity of a variety of normalform transformations for transition diagram systems, which are a parsing view of extended contextfree grammars. A transition diagram system is a finite collection of finitestate machines each of which is labeled with a unique nonterminal symbol. The study is motivated by the implementation project GraMa which will provide a C++ toolkit for the symbolic manipulation of contextfree objects just as Grail does for regular objects. 1 Introduction In the 1960's, extended contextfree grammars (as BackusNaur form) were introduced as a useful abbreviatory notation that made contextfree grammars easier to write. More recently, the Standardized General Markup Language (SGML) [17] used a similar abbreviatory notation to define extended contextfree grammars for documents. Currently, XML [4], which is a simplified version of SGML, is being promoted as the markup language for the web, instead of HTML (a specific grammar or DTD specified us...
Formally verifying data and control with weak reachability invariants
 FORMAL METHOD IN COMPUTERAIDED DESIGN
, 1998
"... Existing formal verification methods do not handle systems that combine state machines and data paths very well. Model checking deals with finitestate machines efficiently, but model checking full designs is infeasible because of the large amount of state in the data path. Theoremproving methods ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Existing formal verification methods do not handle systems that combine state machines and data paths very well. Model checking deals with finitestate machines efficiently, but model checking full designs is infeasible because of the large amount of state in the data path. Theoremproving methods may be effective for verifying data path operations, but verifying the control requires finding and proving inductive invariants that characterize the reachable states of the system. We present a new approach to verification of systems that combine control FSMs and data path operations. Invariants are specified only for a small set of control states, called clean states, where the invariants are especially simple. We avoid the need to specify the invariants for the unclean states by symbolically simulating over all paths to find the possible next clean states. The set of all paths from one clean state to the next is represented by a regular expression, which is extracted from the control FSMs. The number of paths is infinite only if the regular expression contains stars. The method uses a heuristic to generalize the symbolic state to cover all of the paths of the starred expression. We have implemented a prototype tool for guiding an existing symbolic simulator and verification tool and used it successfully to prove properties of the Instruction Fetch Unit of TORCH, a superscalar microprocessor designed at Stanford. With much less effort, we were able to find all the bugs in the unit that were found earlier by manually strengthening the invariants.
A Framework to Visualize Equivalences Between Computational Models of Regular Languages
"... We discuss how to increase and simplify the understanding of the equivalence relations between machine models and/or language representations of formal languages by means of the animation tool SAGEMoLiC. Our new educational tool permits the simulation of the execution of models of computation, as ma ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
We discuss how to increase and simplify the understanding of the equivalence relations between machine models and/or language representations of formal languages by means of the animation tool SAGEMoLiC. Our new educational tool permits the simulation of the execution of models of computation, as many other animation systems do, but its philosophy goes further than these of the usual systems since it allows for a true visualization of the key notions involved in the formal proofs of these equivalences. In contrast with the proposal of previous systems, our approach to visualize equivalence theorems is not a simple "step by step animation" of specific conversion algorithms between computational models and/or grammatical representations of formal languages, because we make emphasis on the key theoretical notions involved in the formal proofs of these equivalences.