Algorithms and lower bounds in finite automata size complexity

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (p. 97-99).In this thesis we investigate the relative succinctness of several types of finite automata, focusing mainly on the following four basic models: one-way deterministic (1)FAs), one-way nondeterministic (1NFAs), two-way deterministic (2DFAS), and two-way nondeterministic (2NFAS). First, we establish the exact values of the trade-offs for all conversions from two-way to one-way automata. Specifically, we prove that the functions ... return the exact values of the trade-offs from 2DFAS to 1DFAS, from 2NFAS to 1DFAs, and from 2DFAs or 2NFAS to 1NFAs, respectively. Second, we examine the question whether the trade-offs from NFAs or 2NFAS to 2DiFAs are polynomial or not. We prove two theorems for liveness, the complete problem for the conversion from 1NFAS to 2DFAS. We first focus on moles, a restricted class of 2NFAs that includes the polynomially large 1NFAS which solve liveness. We prove that, in contrast, 2DFA moles cannot solve liveness, irrespective of size.(cont.) We then focus on sweeping 2NFAS, which can change the direction of their input head only on the end-markers. We prove that all sweeping 2NFAs solving the complement of liveness are of exponential size. A simple modification of this argument also proves that the trade-off from 2DFAS to sweeping 2NFAS is exponential. Finally, we examine conversions between two-way automata with more than one head-like devices (e.g., heads, linearly bounded counters, pebbles). We prove that, if the automata of some type A have enough resources to (i) solve problems that no automaton of some other type B can solve, and (ii) simulate any unary 2DFA that has additional access to a linearly-bounded counter, then the trade-off from automata of type A to automata of type B admits no recursive upper bound.by Christos Kapoutsis.Ph.D

Petri nets for systems and synthetic biology

We give a description of a Petri net-based framework for modelling and analysing biochemical pathways, which uni¯es the qualita- tive, stochastic and continuous paradigms. Each perspective adds its con- tribution to the understanding of the system, thus the three approaches do not compete, but complement each other. We illustrate our approach by applying it to an extended model of the three stage cascade, which forms the core of the ERK signal transduction pathway. Consequently our focus is on transient behaviour analysis. We demonstrate how quali- tative descriptions are abstractions over stochastic or continuous descrip- tions, and show that the stochastic and continuous models approximate each other. Although our framework is based on Petri nets, it can be applied more widely to other formalisms which are used to model and analyse biochemical networks

Translation from Classical Two-Way Automata to Pebble Two-Way Automata

We study the relation between the standard two-way automata and more powerful devices, namely, two-way finite automata with an additional "pebble" movable along the input tape. Similarly as in the case of the classical two-way machines, it is not known whether there exists a polynomial trade-off, in the number of states, between the nondeterministic and deterministic pebble two-way automata. However, we show that these two machine models are not independent: if there exists a polynomial trade-off for the classical two-way automata, then there must also exist a polynomial trade-off for the pebble two-way automata. Thus, we have an upward collapse (or a downward separation) from the classical two-way automata to more powerful pebble automata, still staying within the class of regular languages. The same upward collapse holds for complementation of nondeterministic two-way machines. These results are obtained by showing that each pebble machine can be, by using suitable inputs, simulated by a classical two-way automaton with a linear number of states (and vice versa), despite the existing exponential blow-up between the classical and pebble two-way machines

Recent advances in petri nets and concurrency

CEUR Workshop Proceeding

Petri nets for modelling metabolic pathways: a survey

In the last 15 years, several research efforts have been directed towards the representation and the analysis of metabolic pathways by using Petri nets. The goal of this paper is twofold. First, we discuss how the knowledge about metabolic pathways can be represented with Petri nets. We point out the main problems that arise in the construction of a Petri net model of a metabolic pathway and we outline some solutions proposed in the literature. Second, we present a comprehensive review of recent research on this topic, in order to assess the maturity of the field and the availability of a methodology for modelling a metabolic pathway by a corresponding Petri net

Artificial intelligence and model checking methods for in silico clinical trials

Model-based approaches to safety and efficacy assessment of pharmacological treatments (In Silico Clinical Trials, ISCT) hold the promise to decrease time and cost for the needed experimentations, reduce the need for animal and human testing, and enable personalised medicine, where treatments tailored for each single patient can be designed before being actually administered. Research in Virtual Physiological Human (VPH) is harvesting such promise by developing quantitative mechanistic models of patient physiology and drugs. Depending on many parameters, such models define physiological differences among different individuals and different reactions to drug administrations. Value assignments to model parameters can be regarded as Virtual Patients (VPs). Thus, as in vivo clinical trials test relevant drugs against suitable candidate patients, ISCT simulate effect of relevant drugs against VPs covering possible behaviours that might occur in vivo. Having a population of VPs representative of the whole spectrum of human patient behaviours is a key enabler of ISCT. However, VPH models of practical relevance are typically too complex to be solved analytically or to be formally analysed. Thus, they are usually solved numerically within simulators. In this setting, Artificial Intelligence and Model Checking methods are typically devised. Indeed, a VP coupled together with a pharmacological treatment represents a closed-loop model where the VP plays the role of a physical subsystem and the treatment strategy plays the role of the control software. Systems with this structure are known as Cyber-Physical Systems (CPSs). Thus, simulation-based methodologies for CPSs can be employed within personalised medicine in order to compute representative VP populations and to conduct ISCT. In this thesis, we advance the state of the art of simulation-based Artificial Intelligence and Model Checking methods for ISCT in the following directions. First, we present a Statistical Model Checking (SMC) methodology based on hypothesis testing that, given a VPH model as input, computes a population of VPs which is representative (i.e., large enough to represent all relevant phenotypes, with a given degree of statistical confidence) and stratified (i.e., organised as a multi-layer hierarchy of homogeneous sub-groups). Stratification allows ISCT to adaptively focus on specific phenotypes, also supporting prioritisation of patient sub-groups in follow-up in vivo clinical trials. Second, resting on a representative VP population, we design an ISCT aiming at optimising a complex treatment for a patient digital twin, that is the virtual counterpart of that patient physiology defined by means of a set of VPs. Our ISCT employs an intelligent search driving a VPH model simulator to seek the lightest but still effective treatment for the input patient digital twin. Third, to enable interoperability among VPH models defined with different modelling and simulation environments and to increase efficiency of our ISCT, we also design an optimised simulator driver to speed-up backtracking-based search algorithms driving simulators. Finally, we evaluate the effectiveness of our presented methodologies on state-of-the-art use cases and validate our results on retrospective clinical data

Modelling bacterial regulatory networks with Petri nets

To exploit the vast data obtained from high throughput molecular biology, a variety of modelling and analysis techniques must be fully utilised. In this thesis, Petri nets are investigated within the context of computational systems biology, with the specific focus of facilitating the creation and analysis of models of biological pathways. The analysis of qualitative models of genetic networks using safe Petri net techniques was investigated with particular reference to model checking. To exploit existing model repositories a mapping was presented for the automatic translation of models encoded in the Systems Biology Markup Language (SBML) into the Petri Net framework. The mapping is demonstrated via the conversion and invariant analysis of two published models of the glycolysis pathway. Dynamic stochastic simulations of biological systems suffer from two problems: computational cost; and lack of kinetic parameters. A new stochastic Petri net simulation tool, NASTY was developed which addresses the prohibitive real-time computational costs of simulations by using distributed job scheduling. In order to manage and maximise the usefulness of simulation results a new data standard, TSML was presented. The computational power of NASTY provided the basis for the development of a genetic algorithm for the automatic parameterisation of stochastic models. This parameter estimation technique was evaluated on a published model of the general stress response of E. coli. An attempt to enhance the parameter estimation process using sensitivity analysis was then investigated. To explore the scope and limits of applying the Petri net techniques presented, a realistic case study investigated how the Pho and aB regulons interact to mitigate phosphate stress in Bacillus subtilis. This study made use of a combination of qualitative and quantitative Petri net techniques and was able to confirm an existing experimental hypothesis.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Modelling bacterial regulatory networks with Petri nets

To exploit the vast data obtained from high throughput molecular biology, a variety of modelling and analysis techniques must be fully utilised. In this thesis, Petri nets are investigated within the context of computational systems biology, with the specific focus of facilitating the creation and analysis of models of biological pathways. The analysis of qualitative models of genetic networks using safe Petri net techniques was investigated with particular reference to model checking. To exploit existing model repositories a mapping was presented for the automatic translation of models encoded in the Systems Biology Markup Language (SBML) into the Petri Net framework. The mapping is demonstrated via the conversion and invariant analysis of two published models of the glycolysis pathway. Dynamic stochastic simulations of biological systems suffer from two problems: computational cost; and lack of kinetic parameters. A new stochastic Petri net simulation tool, NASTY was developed which addresses the prohibitive real-time computational costs of simulations by using distributed job scheduling. In order to manage and maximise the usefulness of simulation results a new data standard, TSML was presented. The computational power of NASTY provided the basis for the development of a genetic algorithm for the automatic parameterisation of stochastic models. This parameter estimation technique was evaluated on a published model of the general stress response of E. coli. An attempt to enhance the parameter estimation process using sensitivity analysis was then investigated. To explore the scope and limits of applying the Petri net techniques presented, a realistic case study investigated how the Pho and aB regulons interact to mitigate phosphate stress in Bacillus subtilis. This study made use of a combination of qualitative and quantitative Petri net techniques and was able to confirm an existing experimental hypothesis.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Computational strategies for a system-level understanding of metabolism

Cell metabolism is the biochemical machinery that provides energy and building blocks to sustain life. Understanding its fine regulation is of pivotal relevance in several fields, from metabolic engineering applications to the treatment of metabolic disorders and cancer. Sophisticated computational approaches are needed to unravel the complexity of metabolism. To this aim, a plethora of methods have been developed, yet it is generally hard to identify which computational strategy is most suited for the investigation of a specific aspect of metabolism. This review provides an up-to-date description of the computational methods available for the analysis of metabolic pathways, discussing their main advantages and drawbacks. In particular, attention is devoted to the identification of the appropriate scale and level of accuracy in the reconstruction of metabolic networks, and to the inference of model structure and parameters, especially when dealing with a shortage of experimental measurements. The choice of the proper computational methods to derive in silico data is then addressed, including topological analyses, constraint-based modeling and simulation of the system dynamics. A description of some computational approaches to gain new biological knowledge or to formulate hypotheses is finally provided

Hybrid modeling and optimization of biological processes

Proß S. Hybrid modeling and optimization of biological processes. Bielefeld: Bielefeld University; 2013