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Pcompleteness of cellular automaton Rule 110
 In International Colloquium on Automata Languages and Programming (ICALP), volume 4051 of LNCS
, 2006
"... We show that the problem of predicting t steps of the 1D cellular automaton Rule 110 is Pcomplete. The result is found by showing that Rule 110 simulates deterministic Turing machines in polynomial time. As a corollary we find that the small universal Turing machines of Mathew Cook run in polyn ..."
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We show that the problem of predicting t steps of the 1D cellular automaton Rule 110 is Pcomplete. The result is found by showing that Rule 110 simulates deterministic Turing machines in polynomial time. As a corollary we find that the small universal Turing machines of Mathew Cook run in polynomial time, this is an exponential improvement on their previously known simulation time overhead.
Small weakly universal Turing machines
"... Abstract. We give small universal Turing machines with statesymbol pairs of (6, 2), (3,3) and (2,4). These machines are weakly universal, which means that they have an infinitely repeated word to the left of their input and another to the right. They simulate Rule 110 and are currently the smallest ..."
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Abstract. We give small universal Turing machines with statesymbol pairs of (6, 2), (3,3) and (2,4). These machines are weakly universal, which means that they have an infinitely repeated word to the left of their input and another to the right. They simulate Rule 110 and are currently the smallest known weakly universal Turing machines. Despite their small size these machines are efficient polynomial time simulators of Turing machines. 1
An Associative Processor for Multicomparand Parallel Searching and Its Selected Applications
"... In this paper a multicomparand associative processor is presented. The structure of the processor and its functions are described in detail. The processor works in a combined bitserial/bitparallel mode. Its main component is a multicomparand associative memory with programmable prescription functi ..."
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Cited by 7 (3 self)
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In this paper a multicomparand associative processor is presented. The structure of the processor and its functions are described in detail. The processor works in a combined bitserial/bitparallel mode. Its main component is a multicomparand associative memory with programmable prescription functions. The multicomparand associative search paradigm is shown to be effective in processing complex search problems from many application areas including computational geometry, graph theory and list/matrix computations. Several representative problems, belonging to different complexity classes, and algorithms for them are presented and discussed.
Parallel and sequential optical computing
, 2008
"... We present a number of computational complexity results for an optical model of computation called the continuous space machine. We also describe an implementation for an optical computing algorithm that can be easily defined within the model. Our optical model is designed to model a wide class of ..."
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We present a number of computational complexity results for an optical model of computation called the continuous space machine. We also describe an implementation for an optical computing algorithm that can be easily defined within the model. Our optical model is designed to model a wide class of optical computers, such as matrix vector multipliers and pattern recognition architectures. It is known that the model solves intractable PSPACE problems in polynomial time, and NC problems in polylogarithmic time. Both of these results use large spatial resolution (number of pixels). Here we look at what happens when we have constant spatial resolution. It turns out that we obtain similar results by exploiting other resources, such as dynamic range and amplitude resolution. However, with certain other restrictions we essentially have a sequential device. Thus we are exploring the border between parallel and sequential computation in optical computing. We describe an optical architecture for the unordered search problem of finding a one in a list of zeros. We argue that our algorithm scales well, and is relatively straightforward to implement. This problem is easily parallelisable and is from the class NC. We go on to argue that the optical computing community should focus their attention on problems within P (and especially NC), rather than developing systems for tackling intractable problems. 1
The complexity of model checking for intuitionistic logics
"... and their modal companions ..."
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On the complexity of the equivalence problem for probabilistic automata
 In Proc. of FoSSaCS’12, volume 7213 of LNCS
, 2012
"... Abstract. Deciding equivalence of probabilistic automata is a key problem for establishing various behavioural and anonymity properties of probabilistic systems. In recent experiments a randomised equivalence test based on polynomial identity testing outperformed deterministic algorithms. In this pa ..."
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Abstract. Deciding equivalence of probabilistic automata is a key problem for establishing various behavioural and anonymity properties of probabilistic systems. In recent experiments a randomised equivalence test based on polynomial identity testing outperformed deterministic algorithms. In this paper we show that polynomial identity testing yields efficient algorithms for various generalisations of the equivalence problem. First, we provide a randomized NC procedure that also outputs a counterexample trace in case of inequivalence. Second, we consider equivalence of probabilistic cost automata. In these automata transitions are labelled with integer costs and each word is associated with a distribution on costs, corresponding to the cumulative costs of the accepting runs on that word. Two automata are equivalent if they induce the same cost distributions on each input word. We show that equivalence can be checked in randomised polynomial time. Finally we show that the equivalence problem for probabilistic visibly pushdown automata is logspace equivalent to the problem of whether a polynomial represented by an arithmetic circuit is identically zero. 1
Backward Induction is PTIMEcomplete
"... Abstract. We prove that the computational problem of finding backward induction outcome is PTIMEcomplete. Key words: gametheory, backward induction, computational complexity, finite extensive games 1 ..."
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Abstract. We prove that the computational problem of finding backward induction outcome is PTIMEcomplete. Key words: gametheory, backward induction, computational complexity, finite extensive games 1
Theory Comput Syst DOI 10.1007/s0022401092596 Query Languages for Data Exchange: Beyond Unions of Conjunctive Queries
"... Abstract The class of unions of conjunctive queries (UCQ) has been shown to be particularly wellbehaved for data exchange; its certain answers can be computed in polynomial time (in terms of data complexity). However, this is not the only class with this property; the certain answers to any DATALOG ..."
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Abstract The class of unions of conjunctive queries (UCQ) has been shown to be particularly wellbehaved for data exchange; its certain answers can be computed in polynomial time (in terms of data complexity). However, this is not the only class with this property; the certain answers to any DATALOG program can also can be computed in polynomial time. The problem is that both UCQ and DATALOG do not allow negated atoms, as adding an unrestricted form of negation to these languages yields to intractability. In this paper, we propose a language called DATALOGC(=) that extends DATALOG with a restricted form of negation, and study some of its fundamental properties. In particular, we show that the certain answers to a DATALOGC(=) program can be computed in polynomial time (in terms of data complexity), and that every union of conjunctive queries with at most one inequality or negated relational atom per disjunct, can be efficiently rewritten as a DATALOGC(=) program in the context of data exchange. Furthermore, we show that this is also the case for a syntactic restriction of the class of unions of conjunctive queries with at most two inequalities per disjunct. This syntactic restriction is given by two conditions that are optimal, in the sense that computing certain answers becomes intractable if one removes any of them. Finally, we provide a thorough analysis of the combined complexity of computing certain answers to DATALOGC(=) programs and other related query languages. In particular, we show that this problem is EXPTIMEcomplete for DATALOGC(=), even if one restricts to conjunctive queries with single inequalities, which is a fragment of DATALOGC(=) M. Arenas ()